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).

1, 1, 3, 23, 465, 19834, 1532489, 193746632, 37368959742, 10437763731100, 4054349060577421, 2119978249890808761, 1452950920608600023603, 1276433147589499725385063, 1410464141866494594480406985, 1928819743142477893302566583434, 3218592064882611634798263991387049

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

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

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

Column k=4 of A257463.

Cf. A333900.

Sequence in context: A358069 A116986 A271962 * A171777 A154896 A134050

Adjacent sequences: A268665 A268666 A268667 * A268669 A268670 A268671

Keyword

nonn

Author

Alois P. Heinz, Feb 10 2016

Extensions

Terms a(10) and beyond from Andrew Howroyd, Apr 18 2020

Status

approved