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

Author

Alois P. Heinz, Apr 30 2015

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Row n=5 of A257463.