## Tuesday, April 30, 2013

### 896

896 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7.

896 has a unique representation as a sum of three squares: 896 = 82 + 162 + 242.

896 cannot be expressed as a sum of four non-zero squares.

896 is the sum of six consecutive primes: 896 = 137 + 139 + 149 + 151 + 157 + 163.

896 is the numerical equivalent of the word TWO on a touch-tine telephone.

896 is the number of different moves a rook can make on a chessboard.

Source: Number Gossip

## Monday, April 29, 2013

### 795

795 = 3 x 5 x 53.

795 is a number whose sum of divisors is a fourth power (A006532): 1 + 3 + 5 + 15 + 53 + 159 + 265 + 795 = 1296 = 64.

795 is the smallest multiple of 5 with a digit sum of 21 (A069534).

795 is the sum of seven positive fifth powers (A003352).

795 is a divisor of 234 - 1.

795 has the representation 795 = 36 + 66.

## Friday, April 26, 2013

### 969

969 = 3 x 17 x 19.

969 and 970 have three distinct prime factors (A140077).

969 is the 17th tetrahedral number (A000292). It is the smallest multidigit tetrahedral palindrome.

969 is a nonagonal number (A001106).

The 18th Mersenne prime has 969 digits (A028335).

The sum of the digits of 969 equals the number of digits times 8 (A061425).

Source: Number Gossip

## Thursday, April 25, 2013

### 2181

2181 = 3 x 727. It is an odd number with two distinct palindromic prime factors (A046404).

2181, 2182, and 2183 are each the product of two primes (semiprimes) (A056809).

The sum of 2181 and the 2181st prime (19,231) produces a palindrome (A115884): 2181 + 91231 = 21412.

2181 is the maximum length of a non-crossing path on a 34 x 34 square lattice (A049486).

2181 has the representation 2181 = 37 - 1.

2181 is a divisor of 4611 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, April 24, 2013

### 786

786 = 2 x 3 x 131. It is the product of three distinct Sophie Germain primes (A157346).

786 is a number n such that n2 (617796) has the property that the sum of its digits (36 = 62) and the product of its digits are nonzero squares (A061268).

786 is an even number that is not the sum of a pair of twin primes (A007534).

786 and the 786th prime (6029) have only the digit 6 in common (A107937).

786 is the sum of six positive cubes in exactly three ways (A048931).

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, April 23, 2013

### 337

337 is a prime number.

337 is a centered dodecagonal number.

813 + 1623 = 97.

337 has a representation as a sum of two squares: 337 = 92 + 162.

337 is the hypotenuse of a primitive Pythagorean triple: 3372 = 1752 + 2882.

337 is a divisor of 87 - 1.

Source: Prime Curios!

## Monday, April 22, 2013

### 864

864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3.

864 is the number of integer partitions of 38 into distinct parts.

864 is the sum of a twin prime pair: 864 = 431 + 433.

864 is the sum of six consecutive prime numbers: 864 = 131 + 137 + 139 + 149 + 151 + 157.

864 is a concentric hexagonal number (A032528).

## Friday, April 19, 2013

### 963

963 = 3 x 3 x 107.

963 is the sum of the first 24 primes (A007504). It is the smallest composite number that is a sum of 24 distinct primes (A073619).

963 is a number n such that the digits of n2 (927369), reversed, include the digits of n as a substring (A115761).

963 and 964 both have six divisors (A049103).

963 is the sum of two consecutive semiprimes (A173966): 963 = 478 + 485.

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, April 18, 2013

### 398

398 = 2 x 199.

398 is the number of integers with integer complexity 22.

398 is the solution to the postage problem with two denominations and 37 stamps (A014616).

398 is a number n such that n10 + n9 + n8 + n7 + n6 + n5 + n4 + n3 + n2 + n + 1 is prime (A162862).

398 is the smallest even number with digit sum 20 (A069532).

398 and the 398th prime (2729) have only the digit 9 in common (A107940).

## Wednesday, April 17, 2013

### 1446

1446 = 2 x 3 x 241.

1446 is 666 in base 15.

1446 is the number of graphs with with 9 vertices and 5 edges.

1446 is the squarefree sum of two successive primes (A206329): 1446 = 719 + 727.

1446 is a number n such that 1 + n + n3 + n5 + n7 + n9 + n11 + n13 is a prime (A124164).

## Tuesday, April 16, 2013

### 1386

1386 = 2 x 3 x 3 x 7 x 11.

1386 is the smallest number n such that n and 6n (6 x 1386 = 8316) are anagrams.

1386 = 1 + 34 + 8 + 64.

1386 is an octagonal pyramidal number (A002414).

1386 is the number of ways of writing 59 as a sum of 9 nonnegative cubes (A173682).

Source: Number Gossip

## Monday, April 15, 2013

### 2007

2007 = 3 x 3 x 223.

2007 divides the sum of the digits of 22007 x 2007!

2007 is a number n such that 25n +1 is a square (A219259).

The sum of the base 2 digits of 2007 (1 + 1 + 1 + 1 + 1 + 0 + 1 + 0 + 1 + 1 + 1 = 9) equals the sum of the base 10 digits of 2007 (2 + 0 + 0 + 7 = 9) (A037308).

2007 is a pentadecagonal number (A051687).

2007 is the smallest of three consecutive numbers, each divisible by a square (A070258).

## Friday, April 12, 2013

### 721

721 = 7 x 103.

721 is a centered hexagonal number (A003215).

721 is the smallest number that can be written as the difference of two positive cubes in two ways (A014440).

721 is the sum of nine consecutive primes: 721 = 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101.

721 is the sum of the factorials of the digits of 16 (A061602): 721 = 6! + 1!

## Thursday, April 11, 2013

### 1080

1080 = 2 x 2 x 2 x 3 x 3 x 3 x 5.

1080 is a pentagonal number (A000326).

1080 is the smallest number with 18 divisors. The sum of the divisors of 1080 is a square (A006532).

1080 is the sum (in degrees) of the internal angles of an eight-sided polygon.

1080 is a number that can be expressed as the difference of the squares of primes in just two distinct ways (A090788).

## Wednesday, April 10, 2013

### 708

708 = 2 x 2 x 3 x 59.

708 is the maximum value of n so that there exist four denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps (A001209).

708 is a decagonal pyramidal number (A007585).

708 is the number of different equations that can be made by summing numbers from 1 to 10 and using every number not more than once (A161943).

708 is the sum of the first 29 composite numbers (A053767).

## Tuesday, April 9, 2013

### 838

838 = 2 x 419. It is a palindrome with exactly two prime factors (A046328). Both prime factors are distinct Sophie Germain primes (A157344). The sum of its prime factors is a prime (A108605): 2 + 419 = 421.

838 is a happy number.

838 and 8382 = 702244 have the same digit sum (A058369).

838 is the number of primes between 140,000 and 150,000 (A038824).

838 is the integer part of the surface area of a regular tetrahedron with edge length 22 (A171972).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, April 8, 2013

### 1744

1744 = 2 x 2 x 2 x 2 x 109.

1744 has a representation as a sum of two squares: 1744 = 122 + 402.

1744 is a divisor of 334 - 1.

1744 is a multiple of 8 that has a digit sum that is a multiple of 8 (A216997).

1744 is a non-palindromic balanced number: the sum of its first two digits equals the sum of its last pair of digits (A145808).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, April 5, 2013

### 583

583 = 11 x 53.

583 is the sum of the first 27 nonprimes (A051349).

583 is the first integer n such that 47 x 2n + 1 is prime.

583 is the least integer that is not a sum or difference of two integers such that all their prime factors are 2, 3, and 5.

583 is the smallest number whose reciprocal has period 26.

583 is the sum of six positive fifth powers: 583 = 35 + 35 + 25 + 25 + 25 + 15.

Source: Prime Curios!

## Thursday, April 4, 2013

### 1543

1543 is a prime number.

1543 = 1111 + 55 + 44 + 333.

1543 is the sum of five positive fifth powers (A003350): 1543 = 45 + 35 + 35 + 25 + 15.

1543 is the sum of 11 consecutive primes (A127338): 1543 = 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167.

1543 is a prime sandwiched between two numbers (1542 and 1544) having the same number of divisors (A067889).

The Köstritzer brewery in Germany was founded in the year 1543.

Source: Prime Curios!

## Wednesday, April 3, 2013

### 639

639 = 3 x 3 x 71.

639 is the sum of the first 20 primes.

639 is the smallest number that is the sum of the first several primes and is congruent with 3 modulo 4.

639 is a number n whose fifth root has a decimal part that begins with n.

639 has the representation 639 = 36 - 90.

Source: Number Gossip

## Tuesday, April 2, 2013

### 9866

9866 = 2 x 4933.

9866 has a representation as a sum of two squares: 9866 = 292 + 952.

9866 is the number of words of length 45 in a certain language (A005819).

9866 is the sum of the proper divisors of the number of partitions of 34 (A139055).

9866 is the number of 6 x 6 arrays of squares of integers, symmetric about both diagonal and antidiagonal with all rows summing to 26 (A156389 and A156485).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, April 1, 2013

### 1473

1473 = 3 x 491.

1473 is an odd number whose sum of prime factors is palindromic (A046353): 3 + 491 = 494.

1473 is a semiprime (A001358) that is the sum of a semiprime k and the kth semiprime (A100467).

1473 is the number of lattice points inside the right triangle with legs 16 x 3 and 16 x 4 (and hypotenuse 16 x 5) (A126587).

1473 is the sum of the digit reversals of the first 41 natural numbers (A062918).

1473 is the smallest number that can be expressed as the sum of distinct Lucas numbers (A000204) in exactly 27 ways (A055635).

The leftmost digit of 1473 gives the number of even digits in 1473 and the rightmost digit of 1473 gives the number of odd digits in the number (A107837).

Mathematician and astronomer Nicolaus Copernicus was born in the year 1473.

Source: On-Line Encyclopedia of Integer Sequences