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A322435 Number of pairs of factorizations of n into factors > 1 where no factor of the second divides any factor of the first. 9
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, 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, 0, 3, 1, 4, 0, 32, 0, 1, 3, 3, 1, 4, 0, 16, 5, 1, 0, 18, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Table of n, a(n) for n=1..85.

EXAMPLE

The a(36) = 15 pairs of factorizations:

  (2*2*3*3)|(4*9)

  (2*2*3*3)|(6*6)

  (2*2*3*3)|(36)

    (2*2*9)|(6*6)

    (2*2*9)|(36)

    (2*3*6)|(4*9)

    (2*3*6)|(36)

     (2*18)|(36)

    (3*3*4)|(6*6)

    (3*3*4)|(36)

     (3*12)|(36)

      (4*9)|(6*6)

      (4*9)|(36)

      (6*6)|(4*9)

      (6*6)|(36)

MATHEMATICA

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

Table[Length[Select[Tuples[facs[n], 2], !Or@@Divisible@@@Tuples[#]&]], {n, 100}]

CROSSREFS

Cf. A000688, A001055, A050336, A265947, A294068, A305149, A305150, A305193, A317144, A322436, A322437, A322438, A322439, A322440, A322441, A322442.

Sequence in context: A055212 A028422 A064577 * A113949 A318808 A257991

Adjacent sequences:  A322432 A322433 A322434 * A322436 A322437 A322438

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 08 2018

STATUS

approved

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)