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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..87.

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}]

CROSSREFS

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

Sequence in context: A025466 A072769 A322437 * A304572 A070204 A011745

Adjacent sequences:  A322435 A322436 A322437 * A322439 A322440 A322441

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 08 2018

STATUS

approved

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Last modified July 5 23:36 EDT 2020. Contains 335475 sequences. (Running on oeis4.)