## Thursday, October 31, 2013

### 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

## Wednesday, October 30, 2013

### 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.

## Tuesday, October 29, 2013

### 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

## Monday, October 28, 2013

### 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).

## Friday, October 25, 2013

### 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

## Thursday, October 24, 2013

### 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

## Wednesday, October 23, 2013

### 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.

## Tuesday, October 22, 2013

### 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).

## Monday, October 21, 2013

### 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).

## Friday, October 18, 2013

### 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

## Thursday, October 17, 2013

### 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!

## Wednesday, October 16, 2013

### 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

## Tuesday, October 15, 2013

### 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!

## Friday, October 11, 2013

### 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).

## Thursday, October 10, 2013

### 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!

## Wednesday, October 9, 2013

### 1739

1739 = 37 x 47.

1739 has a base 5 representation (23424) that begins with its base 9 representation (2342).

1739 is a value of n for which n8, n9, n10, and 1011 all have the same digit sum.

1739 is a number such that its square is the sum of three successive primes (A076304).

1739 is a number that becomes prime (139, 173, 179, 739) if any one digit is deleted (A034304).

The sum of the digits of 1739 exceeds the sum of the digits of its square (A064399).

## Tuesday, October 8, 2013

### 622

622 = 2 x 311.

622 and 623 are consecutive semiprimes (A070552).

622 is the number of primes less than 4600 (A028505).

622 is the sum of the first 27 composite numbers (A053767).

622 is the sum of no fewer than 17 fourth powers (A099591).

622 is a number whose digit sum is 10 (A052224).

622 has the representation 54 - 3.

622 is a divisor of 9510 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Monday, October 7, 2013

### 1570

1570 = 2 x 5 x 157.

1570 has two representations as a sum of two squares: 1570 = 72 + 392 = 272 + 292.

1570 is a divisor of 1312 - 1.

1570 is the sum of all composite numbers between the 36th and 38th prime numbers (A174520).

1570 uses only the digits 0, 1, 2, 3, and 4 when expressed in every base from 2 to 9.

Source: On-Line Encyclopedia of Integer Sequences

## Friday, October 4, 2013

### 2061

2061 = 3 x 3 x 229.

2061 is the number of pentagons that can be formed with perimeter 52 (partitions of 52 into five parts such that the sum of any four is more than the fifth) (A069906).

2061 has a representation as a sum of two squares: 2061 = 62 + 452.

The 2061st prime is a partition number (A051143).

2061 is the number of sets of distinct positive integers with mean 7 (A066571).

Source: Prime Curios!

## Thursday, October 3, 2013

### 428

428 = 2 x 2 x 107.

428 has the property that its square is the concatenation of two consecutive numbers (A030467): 4282 = 183184.

428 is 654 in base 8. It is 525 in base 9 (A029955).

428 is the number of ways of writing 34 as a sum of 8 nonnegative cubes (A173681).

428 is a heptadecagonal (17-gonal) number (A051869).

## Wednesday, October 2, 2013

### 1440

1440 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5.

1440 is 112200 in base 4.

1440 has a representation as a sum of two squares: 1440 = 122 + 362.

There are exactly 1440 Henry VIII primes.

1440 is a number that can be expressed as the difference of the squares of primes in just one distinct way (A090781).

1440 is the number of essentially different ways of arranging numbers 1 through 14 around a circle so that the sum of each pair of adjacent numbers is prime (A051252).

1440 is the number of minutes in one day.

1440 is the sum of the internal angles of a 10-sided polygon.

A bolt of fabric is 1440 inches in length.

Source: Number Gossip

## Tuesday, October 1, 2013

### 870

870 = 2 x 3 x 5 x 29.

870 is a pronic number (the product of two consecutive integers): 870 = 29 x 30.

870 is the sum its digits plus the cubes of its digits: 870 = 8 + 7 + 0 + 83 + 73 + 03.

870 is 606 in base 12 and 303 in base 17.

870 is the sum of 10 consecutive primes: 870 = 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107.

870 is the magic constant (or sum) for a 12 x 12 normal magic square.

Source: Number Gossip