2014

2014 = 2 x 19 x 53.

2013, 2014, and 2015 each have three distinct prime factors (A168626).

2014 = 13³ - 13² - 13¹ - 13⁰ (A083074).

2014 is 11111011110 in base 2 (binary). It is 133132 in base 4.

2014 is the sum of three distinct nonzero squares in exactly nine ways (A025347).

2014 divides 83¹² - 1.

2014 is the International Year of Crystallography.

Source: On-Line Encyclopedia of Integer Sequences

5714

5714 = 2 x 2857.

5714 is 42242 in base 6 and 22442 in base 7.

5714 is the number of rooted trees with 10 nodes and a single labeled node (A000107).

5714 has a representation as a sum of two squares: 5714 = 35² + 67².

5714 divides 39⁷ - 1.

5714 is the number of intersections between a sphere inscribed in a cube and the 35 x 35 x 35 cubes resulting from a cubic lattice subdivision of the enclosing cube (A085690).

5714 is the number of stereoisomers of all hydrocarbons with 9 nodes (A036672).

Source: On-Line Encyclopedia of Integer Sequences

3388

3388 = 2 x 2 x 7 x 11 x 11.

3388 is 11122111 in base 3. It is 898 in base 20.

3388 and the sum of the digits of 3388 are both multiples of 11 (A216995).

3388 is a concentric heptagonal number (A195041).

3388 is the smallest number requiring 31 chisel strokes for its representation in Roman numerals, with "C" requiring 2 strokes (MMMCCCLXXXVIII) (A002964).

3388 is the sum of three consecutive hexagonal numbers (A129109).

Source: On-Line Encyclopedia of Integer Sequences

2315

2315 = 5 x 463.

2315 divides 21³ - 1.

2315 = 2⁷ + 3⁷ (A007689). It is the sum of the seventh powers of two consecutive primes (A133538).

2315 is a centered cube number (A036085).

2315 is a number n such that n, n + 2, n + 4, n + 6, and n + 8 are semiprimes (A092127).

2315 is the sum of five nonzero 6th powers (A003361).

Source: On-Line Encyclopedia of Integer Sequences

8400

8400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7.

8400 is a number with four distinct prime factors {2, 3, 5, 7} (A147571).

8400 is a pentagonal number (A000326).

8400 is the number of ways of writing 31 as the sum of seven triangular numbers (A226252).

8400 is 1100 in base 20.

8400 is a number that can be expressed as the difference of the squares of primes in just three distinct ways (A090782).

8400 divides 43⁴ - 1.

8400 is the number of legal queen moves in chess.

Source: Number Gossip

8223

8223 = 3 x 2741.

8223 is the smallest number having exactly two odd prime factors that differ by 2 x n², for n = 37 (A190052).

8223 has the representation 8223 = 2¹³ + 31.

8223 divides 65²⁰ - 1.

Source: On-Line Encyclopedia of Integer Sequences

3183

3183 = 3 x 1061.

3183 is the next semiprime after the partial sum of the first 46 semiprimes (A182081).

3183 has the representation 5⁵ + 58.

3183 divides 14²⁰ - 1.

3183 is the smallest number having exactly two odd prime factors that differ by 2 x n², for n = 23 (A190052).

3183 is the maximum number of different determinants that can be produced by permuting the elements of a 3 x 3 matrix with nonnegative entries less than or equal to 13 (A099834).

Source: On-Line Encyclopedia of Integer Sequences

689

689 = 13 x 53.

689 is the smallest strobogrammatic brilliant number. Deleting the middle digit gives the smallest strobogrammatic semiprime (69).

689 is the sum of three consecutive primes and seven consecutive primes: 689 = 227 + 229 + 233 = 83 + 89 + 97 + 101 + 103 + 107 + 109.

689 has two representations as a sum of two squares: 689 = 8² + 25² = 17² + 20².

689 is the hypotenuse of two primitive Pythagorean triples: 689² = 111² + 680² = 400² + 561².

689 is the smallest number that can be written as the sum of three distinct squares in nine ways.

689 is 373 in base 14.

Source: Prime Curios!

897

897 = 3 x 13 x 23. It is the only sphenic number with prime factors of the form p(p + 10)(p + 20).

897 is divisible by the sum of its prime factors (A046346).

897 is a Cullen number; it has the form n x 2ⁿ + 1, for n = 7 (A002064).

897 is the sum of the first 34 nonprimes (A051349).

The sum of the digits of 897 is equal to 8 times the number of digits (A061425).

897 is the sum of three nonzero fourth powers (A003337).

897 divides 47⁴ - 1.

Source: Prime Curios!

2005

2005 = 5 x 401.

2005 is a semiprime that is the sum of four successive semiprimes (A158339).

2005 = 1 + 2 x 3¹ + 3 x 3² + 4 x 3³ + 5 x 3⁴ + 6 x 3⁵ (A113531).

2005 has two representations as a sum of two squares: 2005 = 18² + 41² = 22² + 39².

2005 is the hypotenuse of two primitive Pythagorean triples: 2005² = 1037² + 1716² = 1357² + 1476².

2005 is a divisor of 98⁸ - 1.

2005 and the square of 2005 use only the digits 0, 2, 4, and 5 (A136897).

2005 is considered a vertically symmetric number (A053701).

Source: On-Line Encyclopedia of Integer Sequences

637

637 = 7 x 7 x 13.

637 is a decagonal number.

637 is 777 in base 9. It is 212121 in base 3 and 1600 in base 7.

637 has a representation as a sum of two squares: 637 = 14² + 21².

637³ = 258,474,853 = (258 - 474 + 853)³.

Source: What's Special About This Number?

5415

5415 = 3 x 5 x 19 x 19.

5415 is a number n such that n and its reversal (5145) are both multiples of 15 (A062905).

5415 is a number n such that the sum of the digits of n equals the squarefree part of n (A070274).

5415 is the smallest number n such that 2n + 1, 4n + 1, 6n + 1, 8n + 1, and 10n + 1 are all prime numbers (A124410).

5415 is a number that cannot be written as a sum of three squares.

5415 is a divisor of 68¹² - 1.

Source: On-Line Encyclopedia of Integer Sequences

9595

9595 = 5 x 19 x 101.

9595 is the sum of seven distinct powers of 3 (A038469): 9595 = 3⁸ + 3⁷ + 3⁶ + 3⁴ + 3³ + 3² + 3⁰.

9595 is 14141 in base 9 (A032821).

9595 is a number whose consecutive digits differ by 4 (A048406).

9595 is a year mentioned in the 1969 song "In the Year 2525" by Denny Zager and Rick Evans (A111729).

Source: On-Line Encyclopedia of Integer Sequences

5600

5600 = 2 x 2 x 2 x 2 x 2 x 5 x 5 x 7. It is the product of three distinct primes (A179691).

5600 is a number with 36 divisors (A175746).

5600 is a number such that the number itself and its square use only the digits 0, 1, 3, 5, and 6 (A136843).

5600 is the number of self-complementary graphs with 13 vertices or nodes (A000171).

5600 is a concentric tetradecagonal number (A195145).

5600 is the perimeter a Pythagorean triangle that can be constructed in exactly five different ways (A156687).

Source: What's Special About This Number?

1794

1794 = 2 x 3 x 13 x 23.

1794 is a nonagonal number (A001106).

1794 is a cake number (A000125). 1794 is the number of pieces resulting from 22 planar cuts through a cube (or cake).

1794 is an octagonal pyramidal number (A002414).

1794 has a base 5 representation (24134) that begins with its base 9 representation (2413).

1794 divides 47⁴ - 1.

Source: Number Gossip

1749

1749 = 3 x 11 x 53. It is the product of three distinct Sophie Germain primes A157346). The sum of the three distinct prime factors is itself a prime number, 67 (A176877).

1748, 1749, and 1750 are three consecutive numbers with three distinct prime factors (A168626).

1749 is a member of a the Fibonacci-like sequence beginning with 14 and 11 (A206605).

1749 divides 23⁴ - 1.

1749 is the number of digits in the fourth Cullen prime.

Source: What's Special About This Number?

3736

3736 = 2 x 2 x 2 x 467.

3736 is a member of the Fibonacci-like sequence beginning with 13 and 8 (A206610).

3736 is a number that is the sum of four positive cubes in exactly three ways (A025405).

3736 and 2³⁷³⁶ end with the same three digits (A067865 and A067866).

Source: On-Line Encyclopedia of Integer Sequences

790

790 = 2 x 5 x 79.

790 is the smallest of four consecutive integers divisible by four consecutive primes respectively (A073607 and A072555).

The sum of the digits of 790 exceeds the sum of the digits of the square of 790 (624100) (A064399).

790 and the 790th prime (6053) have only the digit 0 in common (A107931).

790 is the sum of the remainders when the 790th prime (6053) is divided by all preceding integers (A050482).

790 is an aspiring number (A063769).

Source: Number Gossip

806

806 = 2 x 13 x 31.

806 is not the sum of a square, a cube, a fourth power, and a fifth power.

806 expressed in base 3 (1002212) and base 4 (30212) ends in 212. 806 is 11211 in base 5 (A029952).

806 is the sum of 12 positive fifth powers (A003357).

806 is a magic constant of a 6 x 6 magic square composed of consecutive primes (A177434).

806 and the 806th prime (6199) have only the digit 6 in common (A107937).

Source: What's Special About This Number?

610

610 = 2 x 5 x 61.

610 is the 15th Fibonacci number (A000045). It is the smallest Fibonacci number that begins with 6.

610 is 747 in base 9 and 505 in base 11.

610 is the sum of the squares of the divisors of 22 (A001157): 610 = 1² + 2² + 11² + 22².

610 is the number of primes less than 4500 (A028505).

610 is a Markov number.

610 has two representations as a sum of two squares: 610 = 9² + 23² = 13² + 21².

610 is a divisor of 11⁴ - 1.

Source: Number Gossip

4949

4949 = 7 x 7 x 101.

4949 has semiprime digits (A111494).

4949 is a number whose consecutive digits differ by 5 (A048407).

4949 is a composite number that yields a prime whenever a 5 is inserted anywhere except the end (A216167).

4949 is the smallest number that is the sum of four nonnegative cubes in five ways (A076749).

4949 has a representation as a sum of two squares: 4949 = 7² + 70².

4949 has a fourth power that is the sum of four distinct fourth powers (A003294 and A096739).

Source: What's Special About This Number?

5770

5770 = 2 x 5 x 577.

The digits of the square of 5770 each occur twice (A052049): 5770² = 33292900.

5770 is an integer that can be expressed as the sum of consecutive primes in exactly four ways (A054999).

5770 is 141040 in base 5.

The sum of the digits of 5770 equals the sum of the digits of the cube of 5770 (A070276).

5770 has two representations as a sum of two squares: 5770 = 21² + 73² = 27² + 71². 5770 is the sum of 21st prime (73) squared and 21st perfect square (A106587).

5770 divides 57¹² - 1.

Source: On-Line Encyclopedia of Integer Sequences

5410

5410 = 2 x 5 x 541.

5410 is the product of three distinct primes a, b, and c such that a² + b² + c² is the average of a twin prime pair (A176879).

5410 is 41014 in base 6 (A043013).

The sum of the digits of 5410 is a substring of 5410 and the square of 5410 (29,268,100) (A162015).

5410 has two representations as a sum of two squares: 5410 = 9² + 73² = 51² + 53².

Source: On-Line Encyclopedia of Integer Sequences

794

794 = 2 x 397.

794 = 1⁶ + 2⁶ + 3⁶ (A001550 and A000540).

794 is the maximal number of regions obtained by joining 13 points around a circle by straight lines (A000127).

794 is the sum of three distinct positive cubes (A024975): 794 = 9³ + 4³ + 1³.

794 is a powerful number; it is the sum of positive powers of its digits (A007532): 794 = 7² + 9³ + 4².

794 has a representation as a sum of two squares: 794 = 13² + 25².

794 divides 63⁴ - 1.

Source: What's Special About This Number?

849

849 = 3 x 283.

849 is the sum of distinct factorials (A059590): 849 = 6! + 5! + 3! + 2! + 1!

849 is a powerful number; it is the sum of positive powers of its digits (A007532): 849 = 8³ + 4⁴ + 9².

849 is a number n such that n (849) and the nth prime (6569) have only the digit 9 in common (A107940).

849 is the number of tilings of a 3 x 5 board with 1 x 1 and L-shaped tiles (where the L-shaped tiles cover three squares) (A127867).

Every base 5 digit of 849 is a base 9 digit of 849 (A037396): 11344 and 1143.

849 divides 44⁶ - 1.

Source: On-Line Encyclopedia of Integer Sequences

2301

2301 = 3 x 13 x 59.

2301 has the same digits in bases 4 (20331), 5 (33201), and 10 (2301). 2301 is 6465 in base 7.

2301 is a nonagonal number (A001106).

2301 is the number of primitive (period 9) 9-bead necklace structures using a maximum of six different colored beads (A056302).

2301 is the maximum number of regions defined by 23 zigzag lines in the plane when a zigzag line is defined as consisting of two parallal infinite half-lines joined by a straight line segment (A117625).

2301 is a number n such that the square of n is an average of three successive primes (A226146).

Source: On-Line Encyclopedia of Integer Sequences

4511

4511 = 13 x 347.

4511 = 4444 + 55 + 11 + 1.

4511 is the smallest positive number that can be written as the sum of distinct Fibonacci numbers in 51 ways (A013583).

4511 is a structured hexagonal anti-prism number (A100183).

4511 is the sum of 12 positive 7th powers (A003379).

Source: What's Special About This Number?

766

766 = 2 x 383.

766 is a centered pentagonal number (A005891).

766 is the number of series-reduced planted trees with 9 leaves (A000669).

766 is 23332 in base 4.

766 is the sum of 12 consecutive primes: 766 = 41 + 43 + 47 + 53+ 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89.

766 is a number n such that the square of n is the sum of two successive primes (A074924).

766 is the number of unimodular 2 x 2 matrices having all terms in {1, . . ., 17} (A210000).

Source: What's Special About This Number?

9661

9661 is a prime number.

9661 is the lower prime of a difference of 16 between consecutive primes (A031934).

9661 has a representation as a sum of two squares; it is the sum of two consecutive squares (A027862 and A163251): 9661 = 69² + 70².

9661 is the hypotenuse of a primitive Pythagorean triple (A067756 and A140391): 9661² = 139² + 9660².

9661 is a divisor of 26¹⁵ - 1.

Source: On-Line Encyclopedia of Integer Sequences

4178

4178 = 2 x 2089.

4178 is a number such that its digit sum in base 2 (4) and its digit sum in base 10 (20) are in the ratio of 2:10 (A135110).

4178 is the sum of the first 36 palindromes (A046489).

4178 is a composite number such that exactly eight permutations of its digits give primes (A163560).

4178 has a representation as a sum of two squares: 4178 = 37² + 53².

4178 is a divisor of 39¹⁸ - 1.

Source: On-Line Encyclopedia of Integer Sequences

3176

3176 = 2 x 2 x 2 x 397.

3176 is a composite number such that exactly eight permutations of its digits give primes (A163560).

3176 is a number that is divisible by 8 and is the difference of two cubes in at least one way (A038850).

3176 has a representation as a sum of two squares: 3176 = 26² + 50².

3176 = 5⁵ + 51.

3176 is a divisor of 63⁴ - 1.

3176 is a number n such that n plus the nth prime gives a triangular number (A115882).

3176 is the number of 2 x 2 matrices having all terms {1, . . . , 9} and positive determinant (A211059).

Source: On-Line Encyclopedia of Integer Sequences

5169

5169 = 3 x 1723.

5169 is a number that can be written using its own digits in order and by using addition and factorial operators (A195670): 5169 = 5! + (1 + 6)!  + 9.

5169 is a semiprime that is the sum of distinct factorials (A115646).

5169 is the sum of the divisors of twice a square number (A065765): 2 x 41² = 3362 and 5169 = 1 + 2 + 41 + 82 + 1681 + 3362.

5169 is a divisor of 41⁶ - 1.

5169 is the lowest common multiple of 3 and n² + n + 1 for n = 41 (A130723).

Source: What's Special About This Number?

2044

2044 = 2 x 2 x 7 x 73.

2044 is the number of rectangles with corners on a 9 x 9 grid of points.

2044 is the sum of the cubes of the divisors of 12 (A001158 and A034660): 2044 = 1³ + 2³ + 3³ + 4³ + 6³ + 12³.

2044 is a number n such that the sum of the cubes of the divisors of n is divisible by n (A046763).

2044 has the representation 2¹¹ - 4 (A028399).

2044 is a divisor of 81³ - 1.

2044 is a year in which the month of February will have five Mondays (A135795).

Source: What's Special About This Number?

840

840 = 2 x 2 x 2 x 3 x 5 x 7.

840 is the least common multiple of the first 8 positive integers (it is the smallest number divisible by 1 through 8).

840 is the smallest number with exactly 32 divisors (A005179 and A037992).

840 is is 11330 in base 5 and 1133 in base 9.

840 is the sum of a twin prime pair (A054735): 840 = 419 + 421.

840 is the sum of distinct factorials (A059590): 840 = 6! + 5!

840 is the smallest positive even integer that is an unordered sum of two primes in exactly 51 ways (A023036).

Source: What's Special About This Number?

9090

9090 = 2 x 3 x 3 x 5 x 101.

9090 has two representations as a sum of two squares: 9090 = 21² + 93² = 39² + 87².

9090 is a divisor of 91⁴ - 1.

9090 is the number of centered 6-valent trees with 16 nodes (A036651).

Source: On-Line Encyclopedia of Integer Sequences

5597

5597 = 29 x 193.

5597 has a cube with only odd digits (A030099 and A085597): 5597³ = 175,333,911,173.

5597 is the number of binary rooted trees with 16 nodes and height exactly 8 (A036597).

5597 is a composite number n such that every divisor (except 1) of n contains the digit 9 (A062680).

5597 has two representations as a sum of two squares: 5597 = 11² + 74² = 46² + 59².

5597 is the hypotenuse of two primitive Pythagorean triples: 5597² = 1365² + 5428² = 1628² + 5355².

5597 is a divisor of 12²⁴ - 1.

Source: What's Special About This Number?

3680

3680 = 2 x 2 x 2 x 2 x 2 x 5 x 23.

3680 is 1155 in base 15 (A033013).

3680 is the number of ways of writing 34 as the sum of 5 squares (A000132).

3680 is a divisor of 47⁴ - 1.

3680 is the number of binary strings of length n with no substrings equal to 0000 0010 or 0100 (A164417).

3680 is the number of cribbage hands with score 24 (A143133).

Source: On-Line Encyclopedia of Integer Sequences

744

744 = 2 x 2 x 2 x 3 x 31.

744 is the number of perfect squared rectangles of order 14 (A002839).

744 is 2112 in base 7.

744 is the sum of four consecutive primes (A034963): 744 = 179 + 181 + 191 + 193.

744 is the number of partitions of 49 into prime parts (A000607).

744 is the sum of the factorials of the digits of 46 (A061602): 744 = 4! + 6! (A059590).

744 is the number of 6-digit perfect powers (A075308).

Source: What's Special About This Number?

3631

3631 is a prime number.

3631 is 11222111 in base 3. It is 1121 in base 15.

3631 is a divisor of 48²² - 1.

3631 is the smallest of three consecutive primes with a difference of six (A047948 and A122535): 3631, 3637, 3643.

3631 is a number n such that the square of n has the property that the sum of its digits and the product of its digits are nonzero squares (A061268).

Source: On-Line Encyclopedia of Integer Sequences

4569

4569 = 3 x 1523.

4569 is a disdyakis dodecahedral number (A100163).

4569 is the number of base 5 6-digit numbers with adjacent numbers differing by two or less (A126392).

4569 is the number of walks on a simple cubic lattice (A052178).

4569 is the smallest number such that the product of its digits is 45 times the sum of its digits (A126789).

Source: On-Line Encyclopedia of Integer Sequences

791

791 = 7 x 113.

791 is the sum of the first 22 primes (A007505). It is also the sum of seven consecutive primes: 791 = 101 + 103 + 107 + 109 + 113 + 127 + 131.

791 is a centered tetrahedral number (A005894).

791 is a divisor of 15⁴ - 1.

791 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 12.

791 is the sum of consecutive nonsquares (A048395).

791 Ani is an asteroid discovered in 1914 and named after the capital of a medieval Armenian empire.

Source: What's Special About This Number?

1725

1725 = 3 x 5 x 5 x 23.

1725 is a structured deltoidal hexacontahedral number (A100166).

1725 is 122331 in base 4.

1725 is the sum of odd numbers in the range 340 to 349 (A053742).

1725 is the number of numbers with five decimal digits and digit sum 13 (A090580).

1725 is the upper of a pair of consecutive happy numbers (A035503).

Source: What's Special About This Number?

9998

9998 = 2 x 4999.

9998 is the smallest number n for which the concatenation n, (n + 1), . . . (n + 21) is prime (A052079).

9998 is the smallest even number with digit sum 35 (A069532). It is the largest 4-digit semiprime (A098450).

9998 is a number n such that n and the square of n contain only the "looped" digits 0, 4, 6, 8, and 9 (A107626 and A136956).

9998 divides the sum of the digits of all numbers from 1 to 9998 (A114136).

Source: What's Special About This Number?

6420

6420 = 2 x 2 x 3 x 5 x 107.

6420 is a number with even decimal digits in decreasing order (A119261).

6420 is a number n such that n and the square of n (41,216,400) use only the digits 0, 1, 2. 4, and 6.

6420 is the number of balls in a hexagonal pyramid of height 29 taken from hexagonal close-packing (A019298).

The John Deere 6420 was a popular tractor model.

Source: On-Line Encyclopedia of Integer Sequences

671

671 = 11 x 61.

671 is a rhombic dodecahedral number.

671 is the 3-digit composite number (k) that yields the greatest percentage of primes from Leonhard Euler's formula x² + x + k (453 out of 1000 possible primes).

671!/176! + 1 is prime.

671 is the magic constant for an 11 x 11 normal magic square.

671 is the solution for the n-queens problem, for n = 11.

671 is a divisor of 9⁵ - 1.

Source: Prime Curios!

7627

7627 = 29 x 263.

7627 is the sum of seven distinct powers of three (A038469).

7627 is a number n such that sigma(n) divides sigma(phi(n)); sigma(phi(n))/sigma(n) = 2 (A066831 and A067382).

7627 is 11414 is base 9 (A032821).

7627 is the number of binary strings of length 22 with no substrings equal to 0001 0010 or 1101 (A164452).

7627 has exactly 7 1s when represented in base 3 (A023698): 101110111.

Source: On-Line Encyclopedia of Integer Sequences

771

771 = 3 x 257.

771 in base 2 (binary) is a palindrome: 1100000011. It is 30003 in base 4 and 303 in base 16. It is 543 in base 12 and 474 in base 13.

771 is a divisor of 16⁴ - 1.

771 is the sum of three consecutive primes: 771 = 251 + 257 + 263.

771!/177! - 1 is a titanic prime with a prime digital sum and prime length.

771 is the number of intersections when all the diagonals of a regular 14-gon are drawn.

Source: Prime Curios!

1779

1779 = 3 x 593.

1779 is the smallest number whose 4th power has 13 digits. 1779 is the smallest number whose 8th power has at least 27 digits (A130082).

1779 is 12123 in base 6. It is 911 in base 14.

1779 is a number c such that the difference of consecutive cubes (c + 1)³ - c³ is the sum of two positive cubes (A226902).

1779 is the sum of eight nonzero 6th powers (A003364).

1779 is a divisor of 77⁴ - 1.

1779 was a non-leap year beginning and ending on a Friday (A224943).

Source: What's Special About This Number?

739

739 is a prime number.

739 is the smallest prime number that is the sum of distinct primes beginning and ending with the digit 3: 739 = 3 + 353 + 383.

739 is the smallest prime that can be expressed as a sum of powers with the four prime digits as bases and exponents: 739 = 2⁷ + 3⁵ + 5² + 7³.

739 has a base 2 representation (1011100011) that begins with its base 9 representation (1011).

739 is a right-truncatable prime because itself, 73, and 7 are prime numbers.

Source: Prime Curios!