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%I #10 Apr 18 2020 17:18:30
%S 1,1,3,23,465,19834,1532489,193746632,37368959742,10437763731100,
%T 4054349060577421,2119978249890808761,1452950920608600023603,
%U 1276433147589499725385063,1410464141866494594480406985,1928819743142477893302566583434,3218592064882611634798263991387049
%N Number of factorizations of m^4 into n factors, where m is a product of exactly n distinct primes and each factor is a product of 4 primes (counted with multiplicity).
%C Also number of ways to partition the multiset consisting of 4 copies each of 1, 2, ..., n into n multisets of size 4.
%H Andrew Howroyd, <a href="/A268668/b268668.txt">Table of n, a(n) for n = 0..50</a>
%e a(2) = 3: (2*3)^4 = 1296 = 36*36 = 54*24 = 81*16.
%e a(3) = 23: (2*3*5)^4 = 810000 = 100*90*90 = 100*100*81 = 135*100*60 = 150*90*60 = 150*100*54 = 150*135*40 = 150*150*36 = 225*60*60 = 225*90*40 = 225*100*36 = 225*150*24 = 225*225*16 = 250*60*54 = 250*81*40 = 250*90*36 = 250*135*24 = 375*54*40 = 375*60*36 = 375*90*24 = 375*135*16 = 625*36*36 = 625*54*24 = 625*81*16.
%Y Column k=4 of A257463.
%Y Cf. A333900.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Feb 10 2016
%E Terms a(10) and beyond from _Andrew Howroyd_, Apr 18 2020