OFFSET
1,4
EXAMPLE
The a(144) = 20 set multipartitions:
(2*3*4*6) (2*8*9) (2*72) (144)
(2*6)*(2*6) (3*6*8) (3*48)
(2*6)*(3*4) (2*3*24) (4*36)
(3*4)*(3*4) (2*4*18) (6*24)
(2*6*12) (8*18)
(3*4*12) (9*16)
(12)*(2*6) (12)*(12)
(12)*(3*4)
MATHEMATICA
strfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strfacs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
Table[With[{g=GCD@@FactorInteger[n][[All, 2]]}, Sum[Binomial[Length[strfacs[n^(1/d)]]+d-1, d], {d, Divisors[g]}]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2018
STATUS
approved