cp's OEIS Frontend

A323086 Number of factorizations of n into factors > 1 such that no factor is a power of any other (unequal) factor.

%I A323086 #5 Feb 05 2019 01:59:15
%S A323086 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,
%T A323086 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,
%U A323086 2,5,1,14,1,2,4,4,2,5,1,9,3,2,1,11,2,2
%N A323086 Number of factorizations of n into factors > 1 such that no factor is a power of any other (unequal) factor.
%e A323086 The a(72) = 14 factorizations:
%e A323086   (2*2*2*3*3),
%e A323086   (2*2*2*9), (2*2*3*6),
%e A323086   (2*2*18), (2*3*12), (2*6*6), (3*3*8), (3*4*6),
%e A323086   (2*36), (3*24), (4*18), (6*12), (8*9),
%e A323086   (72).
%t A323086 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A323086 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A323086 Table[Length[Select[facs[n],stableQ[Union[#],IntegerQ[Log[#1,#2]]&]&]],{n,100}]
%Y A323086 Cf. A001055, A001597, A002865, A007916, A052410, A101417, A292886, A303707, A305149, A323053, A323087.
%K A323086 nonn
%O A323086 1,4
%A A323086 _Gus Wiseman_, Jan 04 2019