## Friday, December 20, 2013

### 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

## Thursday, December 19, 2013

### 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

## Wednesday, December 18, 2013

### 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

## Tuesday, December 17, 2013

### 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

## Monday, December 16, 2013

### 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

## Friday, December 13, 2013

### 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

## Thursday, December 12, 2013

### 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

## Wednesday, December 11, 2013

### 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!

## Tuesday, December 10, 2013

### 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!

## Monday, December 9, 2013

### 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

## Friday, December 6, 2013

### 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.

## Thursday, December 5, 2013

### 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

## Wednesday, December 4, 2013

### 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

## Tuesday, December 3, 2013

### 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).

## Monday, December 2, 2013

### 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