cp's OEIS Frontend

A322435 Number of pairs of factorizations of n into factors > 1 where no factor of the second divides any factor of the first.

%I A322435 #7 Dec 09 2018 12:27:15
%S A322435 1,0,0,1,0,1,0,2,1,1,0,3,0,1,1,5,0,3,0,3,1,1,0,7,1,1,2,3,0,4,0,7,1,1,
%T A322435 1,15,0,1,1,7,0,4,0,3,3,1,0,16,1,3,1,3,0,7,1,7,1,1,0,18,0,1,3,16,1,4,
%U A322435 0,3,1,4,0,32,0,1,3,3,1,4,0,16,5,1,0,18,1
%N A322435 Number of pairs of factorizations of n into factors > 1 where no factor of the second divides any factor of the first.
%e A322435 The a(36) = 15 pairs of factorizations:
%e A322435   (2*2*3*3)|(4*9)
%e A322435   (2*2*3*3)|(6*6)
%e A322435   (2*2*3*3)|(36)
%e A322435     (2*2*9)|(6*6)
%e A322435     (2*2*9)|(36)
%e A322435     (2*3*6)|(4*9)
%e A322435     (2*3*6)|(36)
%e A322435      (2*18)|(36)
%e A322435     (3*3*4)|(6*6)
%e A322435     (3*3*4)|(36)
%e A322435      (3*12)|(36)
%e A322435       (4*9)|(6*6)
%e A322435       (4*9)|(36)
%e A322435       (6*6)|(4*9)
%e A322435       (6*6)|(36)
%t A322435 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A322435 Table[Length[Select[Tuples[facs[n],2],!Or@@Divisible@@@Tuples[#]&]],{n,100}]
%Y A322435 Cf. A000688, A001055, A050336, A265947, A294068, A305149, A305150, A305193, A317144, A322436, A322437, A322438, A322439, A322440, A322441, A322442.
%K A322435 nonn
%O A322435 1,8
%A A322435 _Gus Wiseman_, Dec 08 2018