A334286 Number of factorizations of m^n into n factors, where m is a product of exactly n distinct primes and each factor is a product of n primes (counted with multiplicity).

1, 1, 2, 10, 465, 190131, 848597563, 43025433375905, 26004966055138634525, 194173310204064149748222455, 18434259996904142171888712495703426, 22778257480946919793779826285286813732062310, 373444566958856976964193391832469245535883039838631492

Offset

0,3

Comments

Also number of ways to partition the multiset consisting of n copies each of 1, 2, ..., n into n multisets of size n.

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = A257462(n,n) = A257463(n,n).

Example

a(3) = 10: (2*3*5)^3 = 2700 = 30*30*30 = 45*30*20 = 50*27*20 = 50*30*18 = 50*45*12 = 75*20*18 = 75*30*12 = 75*45*8 = 125*18*12 = 125*27*8.

Crossrefs

Main diagonal of A257462 and of A257463.

Sequence in context: A013034 A207140 A059723 * A265627 A112449 A011824

Adjacent sequences: A334283 A334284 A334285 * A334287 A334288 A334289

Keyword

nonn

Author

Alois P. Heinz, Apr 21 2020

Extensions

More terms from Andrew Howroyd, Apr 21 2020

Status

approved