## Wednesday, November 27, 2013

### 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.

## Tuesday, November 26, 2013

### 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

## Monday, November 25, 2013

### 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

## Friday, November 22, 2013

### 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).

## Thursday, November 21, 2013

### 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

## Wednesday, November 20, 2013

### 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).

## Tuesday, November 19, 2013

### 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 + 7125770 is the sum of 21st prime (73) squared and 21st perfect square (A106587).

5770 divides 5712 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Monday, November 18, 2013

### 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

## Friday, November 15, 2013

### 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.

## Thursday, November 14, 2013

### 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

## Wednesday, November 13, 2013

### 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

## Tuesday, November 12, 2013

### 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).

## Monday, November 11, 2013

### 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).

## Friday, November 8, 2013

### 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

## Thursday, November 7, 2013

### 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

## Wednesday, November 6, 2013

### 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

## Tuesday, November 5, 2013

### 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).

## Monday, November 4, 2013

### 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).

## Friday, November 1, 2013

### 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).