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A322436 Number of pairs of factorizations of n into factors > 1 where no factor of the second properly divides any factor of the first. 6
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, 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, 33, 3, 12, 1, 8, 3, 12, 1, 67, 1, 3, 8, 8, 3, 12, 1, 39, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

The a(12) = 8 pairs of factorizations:

  (2*2*3)|(2*2*3)

  (2*2*3)|(2*6)

  (2*2*3)|(3*4)

  (2*2*3)|(12)

    (2*6)|(12)

    (3*4)|(3*4)

    (3*4)|(12)

     (12)|(12)

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[Tuples[facs[n], 2], !Or@@divpropQ@@@Tuples[#]&]], {n, 100}]

CROSSREFS

Cf. A000688, A001055, A050336, A265947, A281113, A294068, A303386, A305149, A305150, A305193, A317144, A322435, A322439, A322440, A322441, A322442.

Sequence in context: A331731 A309891 A317937 * A013603 A157892 A264441

Adjacent sequences:  A322433 A322434 A322435 * A322437 A322438 A322439

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 08 2018

STATUS

approved

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Last modified July 11 15:58 EDT 2020. Contains 335626 sequences. (Running on oeis4.)