OFFSET
1,4
LINKS
Wikipedia, Geometric mean
FORMULA
a(2^n) = A067538(n).
EXAMPLE
The a(4) = 2 through a(36) = 5 factorizations (showing only the cases where n is a perfect power).
(4) (8) (9) (16) (25) (27) (32) (36)
(2*2) (2*2*2) (3*3) (2*8) (5*5) (3*3*3) (2*2*2*2*2) (4*9)
(4*4) (6*6)
(2*2*2*2) (2*18)
(3*12)
MATHEMATICA
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], IntegerQ[GeometricMean[#]]&]], {n, 2, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 15 2019
STATUS
approved