## Thursday, February 28, 2013

### 448

448 = 2 x 2 x 2 x 2 x 2 x 2 x 7.

448 is the number of integer partitions of 33 into distinct parts.

448 is the number of 10-iamonds (polyiamonds).

448 is 121121 in base 3.

448 is a refactorable (or tau) number (A033950). The number of divisors of 448 divides 448.

## Wednesday, February 27, 2013

### 392

392 = 2 x 2 x 2 x 7 x 7.

392 is 112112 in base 3. It is 242 in base 13 and 161 in base 17.

392 has a representation as a sum of two squares: 392 = 142 + 142.

392 is the number of ways of making change for 53 cents using coins of 1, 2, 5, 10 cents (A000008).

4392 + 3 is prime.

392 is a Harshad number and a Kaprekar constant in base 5.

Source: Prime Curios!

## Tuesday, February 26, 2013

### 1501

1501 = 19 x 79.

1501 is palindromic in base 2 (binary): 10111011101. It is 535 in base 17.

1501 is a centered pentagonal number (A005891).

1501 is the smallest number representable as the sum of three triangular numbers in exactly 33 ways (A061262).

1501 is a divisor of 566 - 1.

Source: On-Line Encyclopedia of Integer Sequences

## Monday, February 25, 2013

### 489

489 = 3 x 163.

489 is the smallest number ending in 1, 3, 7, or 9 that cannot be made prime by adding any multiple of 100 up to 700. In other words, 589, 689, 789, 889, 989, 1089, and 1189 are all composites.

489 is an octahedral number (A005900).

489 is the number of primes less than 3,500 (A028505).

489 is the sum of five positive fifth powers (A003350): 489 = 35 + 35 + 15 + 15.

Source: Prime Curios!

## Friday, February 22, 2013

### 697

697 = 17 x 41.

697 is a heptagonal number.

697 is a cake number.

697 is a 12-hyperperfect number.

697 has two representations as a sum of two squares: 697 = 112 + 242 = 162 + 212.

697 is the hypotenuse of two primitive Pythagorean triples: 6972 = 1852 + 6722 = 4552 + 5282.

## Thursday, February 21, 2013

### 876

876 = 2 x 2 x 3 x 73.

876 is a dodecagonal pyramidal number.

All the powers of 876 end with 376.

876 is 4020 in base 6. It is 727 in base 11, 525 in base 13, and 282 in base 19.

## Wednesday, February 20, 2013

### 1626

1626 = 2 x 3 x 271.

1626 is a centered pentagonal number.

1626 is the number of binary partitions of 31.

1626 is 2020020 in base 3.

1626 is a divisor of 296 - 1.

## Tuesday, February 19, 2013

### 691

691 is a prime number.

691 is the only known prime number that is a square when turned upside down (169) and another square when reversed (196).

691 is the smallest prime that can be written as the sum of thirteen consecutive primes.

691 is the (negative) numerator of the 12th Bernoulli number (-691/2730).

As conjectured by Ramanujan and proved by G. N.Watson, Ramanujan's tau function is divisible by 691 for almost all positive integers.

Source: Prime Curios!

## Friday, February 15, 2013

### 921

921 = 3 x 307.

921 is 1110011001 in base 2 (binary). It is 32121 in base 4 and 333 in base 17.

921, 922, and 923 are each the product of two primes (A056809).

921 is the sum of nine positive fifth powers (A003354).

921 is the number of 10-digit numbers that are divisible by 510 (A151754).

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, February 14, 2013

### 1527

1527 = 3 x 509.

1527 has the representation  3 x 29 - 9.

1527 is the lower of a pair of consecutive happy numbers (A035502).

1527 is the sum of eight nonzero sixth powers (A003364).

The sum of the distinct prime factors of 1527 is a cube (A164788): 3 + 509 = 512 = 83.

Mathematician John Dee was born in the year 1527.

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, February 13, 2013

### 2087

2087 is a prime number.

2087 and 2089 form a twin prime pair (A071698).

The reverse of 20879 is prime.

2087 is the sum of three distinct positive cubes (A122723).

2087, 28087, and 20887 are all primes (inserting the digit 8 between any two adjacent digits) (A217047).

2,087 is the number of working hours in a year for the purpose of salary conversion between annual salary and hourly rate.

Source: Prime Curios!

## Tuesday, February 12, 2013

### 1426

1426 = 2 x 23 x 31.

1426 is the number of integer partitions of 42 into distinct parts.

1426 is a pentagonal number.

1426 is the smallest number n such that the sum of the divisors of n equals the product of the squares of the digits of n: 1 + 2 + 23 + 31 + 46 + 62 + 713 + 1426 = 2304 = 12 x 42 x 22 x 62.

1426 is 474 in base 18.

1426 is the sum of the totient function for the first 68 integers.

Source: Number Gossip

## Monday, February 11, 2013

### 979

979 = 11 x 89.

979 is a divisor of 344 - 1.

979 is the sum of the first five fourth powers (A000538): 979 = 14 + 24 + 34 + 44 + 54.

979 is 454 in base 15 (A029970).

979 is the sum of 11 consecutive primes (A127338): 979 = 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109.

979 is the sum of 11 positive fifth powers (A003356).

## Friday, February 8, 2013

### 2462

2462 = 2 x 1231. It is a semiprime with even digits (A108636).

2462 is a divisor of 5515 - 1.

2462 is the sum of 26 and the partition number of 26 (A133041).

2462 is the number of configurations of Sam Loyd's sliding block 15-puzzle that require a minimum of 10 moves to be reached, starting with the empty square at one of the eight non-corner boundary squares (A090165).

2462 and 24622 = 6061444 use only the digits 0, 1, 2, 4, and 6 (A136818).

Source: On-Line Encyclopedia of Integer Sequences

## Thursday, February 7, 2013

### 2374

2374 = 2 x 1187.

2374 is the number of primes of the form 2k + 1 less than 105 (A001161).

2374 is a number that is not the sum of a triangular number, a square, and a fourth power (A115159).

2374 is the number of unit square lattice cells inside half-plane (two adjacent quadrants) of an origin-centered circle of diameter 79 (A136515).

2374 is the number of sums S of distinct positive integers satisfying S less than or equal to 31 (A026906).

Source: On-Line Encyclopedia of Integer Sequences

## Wednesday, February 6, 2013

### 1742

1742 = 2 x 13 x 67. It is the first of a pair of sphenic twins (consecutive integers, each the product of three distinct primes (A215217).

1742 is a divisor of 293 - 1.

1742 is 2345 in base 9.

1742 is a number n such that 1 + n + n3 + n5 + . . . + n21 + n23 is prime (A125181).

1742 is a number whose product of digits (56) is four times the sum of the digits (14) (A062036).

1742 is the number of walks of length 6 on a square lattice that start from the origin and do not touch the nonpositive real axis once they have left their starting point (A053791).

In the year 1742, Christian Goldbach conjectured that every even number greater than or equal to 4 can be expressed as the sum of two primes.

Source: On-Line Encyclopedia of Integer Sequences

## Tuesday, February 5, 2013

### 1719

1719 = 3 x 3 x 191.

1719 is the concatenation of the seventh and eighth primes (A045533 and A007795), a pair of twin primes, or two consecutive odd numbers (A032607).

1719 is the largest integer that cannot be written as the sum of squares of integers larger than 16 (A193018).

1719 is the sum of 11 non-zero 6th powers (A003367).

1719 is the smallest number expressible as a sum of 9 cubes (including 0) in 43 ways (A214725).

Source: On-Line Encyclopedia of Integer Sequences

## Monday, February 4, 2013

### 616

616 = 2 x 2 x 2 x 7 x 11.

616 is a heptagonal number (A000566). It is also a tridecagonal number (A051865).

616 is a Padovan number (A000931).

616 is 211211 in base 3. It is 434 in base 12 (A029967).

616 is the sum of eight positive fifth powers (A003353).

Source: On-Line Encyclopedia of Integer Sequences

## Friday, February 1, 2013

### 542

542 = 2 x 271.

542 is a member of the Fibonacci-type sequence starting with 3 and 8.

542 is 20132 in base 4 and 4132 in base 5. It is 392 in base 12 and 329 in base 13.

542 is the number of primes less than 104 having at least one digit 9 (A091710).

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