

A268668


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).


3



1, 1, 3, 23, 465, 19834, 1532489, 193746632, 37368959742, 10437763731100, 4054349060577421, 2119978249890808761, 1452950920608600023603, 1276433147589499725385063, 1410464141866494594480406985, 1928819743142477893302566583434, 3218592064882611634798263991387049
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Also number of ways to partition the multiset consisting of 4 copies each of 1, 2, ..., n into n multisets of size 4.


LINKS



EXAMPLE

a(2) = 3: (2*3)^4 = 1296 = 36*36 = 54*24 = 81*16.
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.


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



