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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
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, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0
OFFSET
1
COMMENTS
First differs from A322437 at a(144) = 4, A322437(144) = 3.
EXAMPLE
The a(240) = 5 pairs of factorizations::
(4*4*15)|(4*6*10)
(6*40)|(15*16)
(8*30)|(12*20)
(10*24)|(15*16)
(12*20)|(15*16)
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
divpropQ[x_, y_]:=And[x!=y, Divisible[x, y]];
Table[Length[Select[Subsets[facs[n], {2}], And[!Or@@divpropQ@@@Tuples[#], !Or@@divpropQ@@@Reverse/@Tuples[#]]&]], {n, 100}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 08 2018
STATUS
approved