

A113941


Pentagonal numbers (A000326) that are also brilliant numbers (A078972).


2



35, 247, 1247, 2501, 4187, 15251, 17767, 33227, 49051, 63551, 68587, 71177, 76501, 81317, 96647, 112477, 118301, 128627, 147737, 159251, 182527, 241001, 250717, 265651, 302177, 318551, 438751, 485357, 563347, 655051, 1563151, 1600117
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OFFSET

1,1


COMMENTS

This is to pentagonal numbers A000326 as A113940 is to triangular numbers A000217. These may be seen as the 5th and 3rd row of an infinite array of kgonal numbers which are also brilliant numbers, where the 4th row is A001248 squares of primes.  Jonathan Vos Post, Apr 05 2009


LINKS



FORMULA



EXAMPLE

a(1) = 35 = 5th pentagonal number = 5*(3*51)/2 = 5 * 7, with the two prime factors each being one digit in length. a(2) = 247 = 13th pentagonal number = 13*(3*131)/2 = 13 * 19, with the two prime factors each being two digits in length. a(6) = 15251 = 101 * 151, with the two prime factors each being three digits in length.  Jonathan Vos Post, Apr 05 2009
17767 is the 109th pentagonal number and 17767=109*163 is brilliant.


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



