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A306268
Number of ways to choose a strict factorization into squarefree factors of each factor in a strict factorization of n.
0
1, 1, 1, 0, 1, 3, 1, 0, 0, 3, 1, 3, 1, 3, 3, 0, 1, 3, 1, 3, 3, 3, 1, 1, 0, 3, 0, 3, 1, 12, 1, 0, 3, 3, 3, 5, 1, 3, 3, 1, 1, 12, 1, 3, 3, 3, 1, 0, 0, 3, 3, 3, 1, 1, 3, 1, 3, 3, 1, 19, 1, 3, 3, 0, 3, 12, 1, 3, 3, 12, 1, 4, 1, 3, 3, 3, 3, 12, 1, 0, 0, 3, 1, 19, 3
OFFSET
1,6
EXAMPLE
The a(216) = 8 factorizations:
(2*3)*(2*3*6) (2*6)*(3*6)
(2)*(2*3)*(3*6) (6)*(2*3*6)
(2)*(3)*(2*3*6) (2)*(6)*(3*6)
(3)*(2*3)*(2*6) (3)*(6)*(2*6)
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Join@@Table[Tuples[Select[facs[#], And[UnsameQ@@#, And@@SquareFreeQ/@#]&]&/@fac], {fac, Select[facs[n], UnsameQ@@#&]}]], {n, 60}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 01 2019
STATUS
approved