cp's OEIS Frontend

A322436 Number of pairs of factorizations of n into factors > 1 where no factor of the second properly divides any factor of the first.

%I A322436 #5 Dec 09 2018 12:27:24
%S A322436 1,1,1,3,1,3,1,5,3,3,1,8,1,3,3,11,1,8,1,8,3,3,1,18,3,3,5,8,1,12,1,15,
%T A322436 3,3,3,31,1,3,3,18,1,12,1,8,8,3,1,39,3,8,3,8,1,18,3,18,3,3,1,42,1,3,8,
%U A322436 33,3,12,1,8,3,12,1,67,1,3,8,8,3,12,1,39,11
%N A322436 Number of pairs of factorizations of n into factors > 1 where no factor of the second properly divides any factor of the first.
%e A322436 The a(12) = 8 pairs of factorizations:
%e A322436   (2*2*3)|(2*2*3)
%e A322436   (2*2*3)|(2*6)
%e A322436   (2*2*3)|(3*4)
%e A322436   (2*2*3)|(12)
%e A322436     (2*6)|(12)
%e A322436     (3*4)|(3*4)
%e A322436     (3*4)|(12)
%e A322436      (12)|(12)
%t A322436 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A322436 divpropQ[x_,y_]:=And[x!=y,Divisible[x,y]];
%t A322436 Table[Length[Select[Tuples[facs[n],2],!Or@@divpropQ@@@Tuples[#]&]],{n,100}]
%Y A322436 Cf. A000688, A001055, A050336, A265947, A281113, A294068, A303386, A305149, A305150, A305193, A317144, A322435, A322439, A322440, A322441, A322442.
%K A322436 nonn
%O A322436 1,4
%A A322436 _Gus Wiseman_, Dec 08 2018