login
A323086
Number of factorizations of n into factors > 1 such that no factor is a power of any other (unequal) factor.
1
1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 6, 2, 2, 2, 4, 1, 5, 1, 3, 2, 2, 2, 9, 1, 2, 2, 6, 1, 5, 1, 4, 4, 2, 1, 9, 2, 4, 2, 4, 1, 6, 2, 6, 2, 2, 1, 11, 1, 2, 4, 4, 2, 5, 1, 4, 2, 5, 1, 14, 1, 2, 4, 4, 2, 5, 1, 9, 3, 2, 1, 11, 2, 2
OFFSET
1,4
EXAMPLE
The a(72) = 14 factorizations:
(2*2*2*3*3),
(2*2*2*9), (2*2*3*6),
(2*2*18), (2*3*12), (2*6*6), (3*3*8), (3*4*6),
(2*36), (3*24), (4*18), (6*12), (8*9),
(72).
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[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[facs[n], stableQ[Union[#], IntegerQ[Log[#1, #2]]&]&]], {n, 100}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 04 2019
STATUS
approved