A325510 Number of non-isomorphic multiset partitions of the multiset of prime indices of n!.

1, 1, 1, 2, 7, 16, 98, 269, 1397, 7582, 70520, 259906, 1677259, 5229112, 44726100, 666355170, 4917007185, 18459879921

Offset: 0

Author

Gus Wiseman, May 08 2019

Keywords

• nonn
• more

Examples

			Non-isomorphic representatives of the a(2) = 1 through a(5) = 16 multiset partitions:
  {{1}}  {{12}}    {{1222}}        {{12333}}
         {{1}{2}}  {{1}{222}}      {{1}{2333}}
                   {{12}{22}}      {{12}{333}}
                   {{2}{122}}      {{13}{233}}
                   {{1}{2}{22}}    {{3}{1233}}
                   {{2}{2}{12}}    {{33}{123}}
                   {{1}{2}{2}{2}}  {{1}{2}{333}}
                                   {{1}{23}{33}}
                                   {{1}{3}{233}}
                                   {{3}{12}{33}}
                                   {{3}{13}{23}}
                                   {{3}{3}{123}}
                                   {{1}{1}{1}{23}}
                                   {{1}{2}{3}{33}}
                                   {{1}{3}{3}{23}}
                                   {{1}{2}{3}{3}{3}}
		

Crossrefs

Cf. A000142, A001055, A007716, A011371, A022559, A076716, A115627, A317791, A318285, A322583, A325272, A325276, A325508, A325509, A325511.

Programs

PARI

\\ Requires C(sig) from A318285.
a(n)={if(n<2, 1, my(f=factor(n!)[,2], sig=vector(vecmax(f))); for(i=1, #f, sig[f[i]]++); C(sig))} \\ Andrew Howroyd, Jan 17 2023

Formula

a(n) = A317791(n!).

a(n) = A318285(A181819(n!)) = A318285(A325508(n)). - Andrew Howroyd, Jan 17 2023

Extensions

a(9)-a(17) from Andrew Howroyd, Jan 17 2023