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A323090
Number of strict factorizations of n using elements of A007916 (numbers that are not perfect powers).
5
1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 2, 1, 2, 2, 0, 1, 2, 1, 2, 2, 2, 1, 2, 0, 2, 0, 2, 1, 5, 1, 0, 2, 2, 2, 3, 1, 2, 2, 2, 1, 5, 1, 2, 2, 2, 1, 2, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 7, 1, 2, 2, 0, 2, 5, 1, 2, 2, 5, 1, 4, 1, 2, 2, 2, 2, 5, 1, 2, 0, 2, 1, 7, 2, 2, 2
OFFSET
1,6
EXAMPLE
The a(72) = 4 factorizations are (2*3*12), (3*24), (6*12), (72). Missing from this list and not strict are (2*2*2*3*3), (2*2*3*6), (2*6*6), (2*2*18), while missing from the list and using perfect powers are (2*36), (2*4*9), (3*4*6), (4*18), (8*9).
MATHEMATICA
radQ[n_]:=Or[n==1, GCD@@FactorInteger[n][[All, 2]]==1];
facssr[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facssr[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], radQ]}]];
Table[Length[facssr[n]], {n, 100}]
CROSSREFS
Positions of 0's are A246547.
Positions of 1's are A000040.
Positions of 2's are A084227.
Positions of 3's are A085986.
Positions of 4's are A143610.
Sequence in context: A177207 A161528 A175083 * A355935 A180026 A136176
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 04 2019
STATUS
approved