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A322438 Number of unordered pairs of factorizations of n into factors > 1 where no factor of one properly divides any factor of the other. 4

%I

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,

%U 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0

%N Number of unordered pairs of factorizations of n into factors > 1 where no factor of one properly divides any factor of the other.

%C First differs from A322437 at a(144) = 4, A322437(144) = 3.

%e The a(240) = 5 pairs of factorizations::

%e (4*4*15)|(4*6*10)

%e (6*40)|(15*16)

%e (8*30)|(12*20)

%e (10*24)|(15*16)

%e (12*20)|(15*16)

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t divpropQ[x_,y_]:=And[x!=y,Divisible[x,y]];

%t Table[Length[Select[Subsets[facs[n],{2}],And[!Or@@divpropQ@@@Tuples[#],!Or@@divpropQ@@@Reverse/@Tuples[#]]&]],{n,100}]

%Y Cf. A001055, A285572, A285573, A303362, A303386, A304713, A305149, A305150, A305193, A316476, A317144, A322435, A322436, A322437, A322442.

%K nonn

%O 1

%A _Gus Wiseman_, Dec 08 2018

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)