OFFSET
1,6
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(60) = 8 factorizations: (2*5*6), (3*4*5), (2*30), (3*20), (4*15), (5*12), (6*10), (60).
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], UnsameQ@@Mean/@primeMS/@#&]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 12 2019
STATUS
approved