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A323087
Number of strict factorizations of n into factors > 1 such that no factor is a power of any other factor.
4
1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 5, 1, 2, 2, 2, 2, 5, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 9, 1, 2, 3, 1, 2, 5, 1, 3, 2, 5, 1, 8, 1, 2, 3, 3, 2, 5, 1, 5, 1, 2, 1, 9, 2, 2, 2
OFFSET
1,6
EXAMPLE
The a(60) = 9 factorizations:
(2*3*10), (2*5*6), (3*4*5),
(2*30), (3*20), (4*15), (5*12), (6*10),
(60).
MATHEMATICA
strfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strfacs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[strfacs[n], stableQ[#, IntegerQ[Log[#1, #2]]&]&]], {n, 100}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 04 2019
STATUS
approved