Friday, October 31, 2014

8666

8666 = 2 x 7 x 619.

8666 has a 9th root whose decimal part starts with the digits 1 to 9 in some order.

8666 is a beastly number (A051003).

8666 is the number of permutations of length 21 that avoid the patterns 123 and 4312 (A116699).

8666 is a number n such that n, n + 1, n + 2, and n + 3 are not divisible by any of their nonzero digits (A244358).

8666 is a number n such that n ends with 6 and is the difference of cubes in at least one way (A038861).

Thursday, October 30, 2014

2430

2430 = 2 x 3 x 3 x 3 x 3 x 3 x 5.

2430 is the number of unordered ways to write 1 as a sum of reciprocals of integers no larger than 18.

2430 is 3300 in base 9.

2430 is the sum of two powers of 3 (A055235).

2430 is the product of all distinct numbers formed by permuting digits of 2430 (A061147).

2430 is a number divisible by the square of the sum of its digits (A072081).

2430 divides 9127 - 1.

Wednesday, October 29, 2014

3564

3564 = 2 x 2 x 3 x 3 x 3 x 3 x 11.

3564 is 11220000 in base 3.

3564 is a concentric hendecagonal number (A195043).

3564 is both an abundant number and a Smith number (A098835).

3564 is a number n such that n together with its double and triple contain every digit (A120564).

3564 divides 8918 - 1.

3564 divides 11 + 22 + 33 + . . . + 35643564 (A135189).

Tuesday, October 28, 2014

5675

5675 = 5 x 5 x 227.

5675 is the number of monic polynomials of degree 13 with integer coefficients whose complex roots are all in the unit disk (A051894).

5675 is 2777 in base 13.

5675 is an alternating sum of decreasing powers (A083326).

Monday, October 27, 2014

3387

3387 = 3 x 1129.

3387 is the largest of three consecutive semiprimes (A115393).

3387 is the number of different keys with 7 cuts, depths between 1 and 7 and depth difference at most 1 between adjacent cut depths (A002714).

3387 and 33387 end with the same two digits (A067749).

3387 divides 318 - 1.

Source: OEIS

Friday, October 24, 2014

5102

5102 = 2 x 2551.

5102 is a semiprime whose digit sum is a perfect cube (A245021).

5102 divides 516 - 1.

5102 is 6888 in base 9 (A043487).

Source: OEIS

Thursday, October 23, 2014

1295

1295 = 5 x 7 x 37.

1295 is 5555 in base 6 (A097252).

1295 has the representation 64 - 1 (A123865 and A024062). It is a subperfect power (A045542).

1295 is the sum of consecutive cubes (A217843).

1295 is the difference of two positive fourth powers (A147857).

Every run of digits of 1295 in base 4 has length 2 (A033002): 110033.

Wednesday, October 22, 2014

8123

8123 is a prime number.

8123 is a prime that can be written as a sum of 13 consecutive primes (A127341).

8123 is a prime p such that q - p = 24, where q is the next prime after p (A098974).

8123 represented in base 4 has 2 2s and 4 3s (A045147): 1332323.

8123 is a prime with an equal number of 0s, 1s, and 2s in its base three representation (A174976): 102010212.

8123 is a prime, as is 812318123281233812348123581236812378123881239 (A244271).

Source: OEIS

Tuesday, October 21, 2014

1845

1845 = 3 x 3 x 5 x 41.

1845 is a number that can be expressed as the difference of the squares of primes in just one distinct way (A090781).

1845 is the number of ways to place three points on a triangular grid of side 7 so that no two of them are adjacent (A238569).

1845 is the sum of 11 nonzero 6th powers (A003367).

1845 has two representations as a sum of two squares: 1845 = 92 + 422 = 182 + 392.

1845 divides 734 - 1.

Source: OEIS

Monday, October 20, 2014

1837

1837 = 11 x 167.

1837 is a centered dodecagonal number (or a star number) (A003154).

1837 is a concentric hexagonal number (A032528).

1837 is a value of n for which 2n (3674) and 7n (12859) together use each of the digits 1 to 9 exactly once.

1837, 1838, and 1839 are consecutive semiprimes (A056809).

1837 is the number of intersections of diagonals in the interior of a regular 18-gon (A006561).

Friday, October 17, 2014

3203

3203 is a prime number.

Reversing the digits of 3203 also produces a prime (A109309).

3203 has the property that if each digit is replaced by its square, the resulting number is a square.

3203 is a prime whose digit sum is 8 (A062343).

3203 is the smallest prime whose decimal expansion begins with concatenation of the first two primes in descending order (A171154).

Thursday, October 16, 2014

9199

9199 is a prime number (A020457).

9199 is a prime whose digit sum is the perfect number 28 (A048517).

9199 is a prime number with every digit a perfect square (A061246).

9199 and the square of 9199 have the same digit sum (A058370).

9199 is the sum of 15 consecutive primes (A161612).

9199 is 243244 in base 5.

9199 divides 4021 - 1.

9199 is a number that cannot be written as a sum of three squares.

Source: OEIS

Wednesday, October 15, 2014

6488

6488 = 2 x 2 x 2 x 811.

6488 would be prime if preceded and followed by 1, 3, 7, or 9 (A059677).

6488 is the maximum number of regions into which 47 triangles divide the plane (A077588).

6488 is a number n such that n! has a square number of digits (A006488).

6488 divides 1518 - 1.

6488 is 22220022 in base 3. It is 8808 in base 9 (A097255 and A043487).

Tuesday, October 14, 2014

2179

2179 is a prime number.

2179 is a lonely number; it sets a new record for the distance to the closest prime (A051650). It is the smallest number a distance 18 from the nearest prime (A051652).

2179 divides 6122 - 1.

2179 is a Wedderburn-Etherington number (A001190).

Friday, October 10, 2014

2854

2854 = 2 x 1427.

2854 is a semiprime with a prime sum of factors (A108605) and with a prime sum of decimal digits (A108610).

2854 is the smallest number that can be written as a sum of distinct Fibonacci numbers in 48 ways (A013583).

2854 is a semiprime s such that s + 3 and s - 3 are both primes (A176140).

Source: OEIS

Thursday, October 9, 2014

3201

3201 = 3 x 11 x 97.

3201 is an octagonal number (A000567).

3201 is the number of regions in a regular 33-gon that are hexagons (A067153).

3201 is the sum of the first 22 Sophie Germain primes (A066819).

3201 divides 982 - 1.

3201 is 12222 in base 7.

Source: OEIS

Wednesday, October 8, 2014

3981

3981 = 3 x 1327.

3981 is the largest number whose fifth power has 18 digits (A114323).

3981 is 111411 in base 5.

3981 is a power of the fifth root of 100, rounded to the nearest integer (A205770).

The aliquot divisors of 3981 sum to a cube (A048698).

Source: OEIS

Tuesday, October 7, 2014

7740

7740 = 2 x 2 x 3 x 3 x 5 x 43.

7740 is a pentagonal number (A049452). It is a pentagonal number that is not the difference of two larger pentagonal numbers (A136113), but it is the sum of two other positive pentagonal numbers (A136117).

7740 is 55500 in base 6 (A097252).

7740 is the number of primes less than 13! (A133228).

7740 is the sum of the interior angles of a 45-sided polygon in degrees (A066164).

7740 divides 496 - 1.

Source: Number Gossip

Monday, October 6, 2014

1833

1833 = 3 x 13 x 47.

1833 is the first of two consecutive sphenic numbers (A215217).

The 1833rd triangular number is palindromic (A008509): 1680861.

1833 is the start of the first run of exactly 7 consecutive odd composite numbers (A075067).

1833 divides 956 - 1.

Source: OEIS

Friday, October 3, 2014

3839

3839 = 11 x 349.

3839 is 120210012 in base 3, the concatenation of three permutations of the digits 0, 1, 2.

3839 is the sum of 11 distinct powers of 2 (A038462).

3839 is the difference between two double factorials (A111300).

3839 is the concatenation of two consecutive numbers (A001704 and A127421).

3839 divides 6729 - 1.

3839 is a number that cannot be written as a sum of three squares.

Source: OEIS

Thursday, October 2, 2014

6306

6306 = 2 x 3 x 1051.

6306 is the sum of three consecutive semiprimes (A173968).

6306 divides 5525 - 1.

6306 is the first of a triplet of consecutive squarefree numbers each of which has exactly three distinct prime factors (A242606).

Source: OEIS

Wednesday, October 1, 2014

8775

8775 = 3 x 3 x 3 x 5 x 5 x 13.

8775 = (25 x 26 x 27)/2 (A027480).

8775 divides 8212 - 1.

8775 is a number that cannot be written as a sum of three squares.

Source: OEIS