A253263 Number of factorizations of m^n into 5 factors, where m is a product of exactly 5 distinct primes and each factor is a product of n primes (counted with multiplicity).

1, 1, 73, 1417, 19834, 190131, 1398547, 8246011, 40837569, 174901563, 664006236, 2274999093, 7139338769, 20758868781, 56466073587, 144806582536, 352420554194, 818441723112, 1822255658908, 3905392549491, 8084697432576, 16214886608495, 31590986308810, 59926495673780

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Example

a(2) = 73: (2*3*5*7*11)^2 = 5336100 = 25*22*22*21*21 = 33*25*22*21*14 = 33*33*25*14*14 = 35*22*22*21*15 = 35*33*22*15*14 = 35*33*22*21*10 = 35*33*33*14*10 = 35*35*22*22*9 = 35*35*33*22*6 = 35*35*33*33*4 = 49*22*22*15*15 = 49*25*22*22*9 = 49*33*22*15*10 = 49*33*25*22*6 = 49*33*33*10*10 = 49*33*33*25*4 = 55*22*21*15*14 = 55*22*21*21*10 = 55*33*15*14*14 = 55*33*21*14*10 = 55*35*22*14*9 = 55*35*22*21*6 = 55*35*33*14*6 = 55*35*33*21*4 = 55*49*22*10*9 = 55*49*22*15*6 = 55*49*33*10*6 = 55*49*33*15*4 = 55*55*14*14*9 = 55*55*21*14*6 = 55*55*21*21*4 = 55*55*49*6*6 = 55*55*49*9*4 = 77*22*15*15*14 = 77*22*21*15*10 = 77*25*22*14*9 = 77*25*22*21*6 = 77*33*15*14*10 = 77*33*21*10*10 = 77*33*25*14*6 = 77*33*25*21*4 = 77*35*22*10*9 = 77*35*22*15*6 = 77*35*33*10*6 = 77*35*33*15*4 = 77*55*14*10*9 = 77*55*15*14*6 = 77*55*21*10*6 = 77*55*21*15*4 = 77*55*35*6*6 = 77*55*35*9*4 = 77*77*10*10*9 = 77*77*15*10*6 = 77*77*15*15*4 = 77*77*25*6*6 = 77*77*25*9*4 = 121*15*15*14*14 = 121*21*15*14*10 = 121*21*21*10*10 = 121*25*14*14*9 = 121*25*21*14*6 = 121*25*21*21*4 = 121*35*14*10*9 = 121*35*15*14*6 = 121*35*21*10*6 = 121*35*21*15*4 = 121*35*35*6*6 = 121*35*35*9*4 = 121*49*10*10*9 = 121*49*15*10*6 = 121*49*15*15*4 = 121*49*25*6*6 = 121*49*25*9*4.

Crossrefs

Row n=5 of A257463.

Sequence in context: A232297 A008392 A221479 * A098676 A056214 A197216

Adjacent sequences: A253260 A253261 A253262 * A253264 A253265 A253266

Keyword

nonn

Author

Alois P. Heinz, Apr 30 2015

Status

approved