OFFSET
1,4
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
LINKS
EXAMPLE
The a(440) = 21 multiset partitions of {1,1,1,3,5}:
{1}{1}{1}{3}{5} {1}{1}{1}{35} {1}{1}{135} {1}{1135} {11135}
{1}{1}{13}{5} {1}{11}{35} {11}{135}
{1}{11}{3}{5} {11}{13}{5} {111}{35}
{1}{1}{3}{15} {1}{13}{15} {113}{15}
{11}{3}{15} {13}{115}
{1}{3}{115} {3}{1115}
{1}{5}{113} {5}{1113}
{3}{111}{5}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[n], And@@(OddQ[Times@@primeMS[#]]&/@#)&]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 08 2022
STATUS
approved