OFFSET
1,4
COMMENTS
LINKS
EXAMPLE
The a(1440) = 6 factorizations into factors all having the same sum of prime indices:
(10*12*12)
(5*6*6*8)
(9*10*16)
(30*48)
(36*40)
(1440)
The a(900) = 5 multiset partitions with equal block-sums:
{{1,1,2,2,3,3}}
{{3,3},{1,1,2,2}}
{{1,2,3},{1,2,3}}
{{1,3},{1,3},{2,2}}
{{3},{3},{1,2},{1,2}}
MATHEMATICA
hwt[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>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], SameQ@@hwt/@#&]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 10 2018
STATUS
approved