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A322437 Number of unordered pairs of factorizations of n into factors > 1 where no factor of one divides any factor of the other. 5
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 A322438 at a(144) = 3, A322438(144) = 4.

LINKS

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

EXAMPLE

The a(240) = 4 pairs of factorizations:

   (6*40)|(15*16)

   (8*30)|(12*20)

  (10*24)|(15*16)

  (12*20)|(15*16)

The a(1728) = 14 pairs of factorizations:

    (6*6*48)|(27*64)

   (6*12*24)|(27*64)

     (6*288)|(27*64)

    (8*8*27)|(12*12*12)

  (12*12*12)|(27*64)

  (12*12*12)|(32*54)

    (12*144)|(27*64)

    (12*144)|(32*54)

    (16*108)|(24*72)

     (18*96)|(27*64)

     (24*72)|(27*64)

     (24*72)|(32*54)

     (27*64)|(36*48)

     (32*54)|(36*48)

MATHEMATICA

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

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

CROSSREFS

Cf. A000688, A001055, A285572, A285573, A294068, A303362, A304713, A305149, A305150, A305193, A316476, A317144, A322435, A322436, A322442.

Sequence in context: A025469 A025466 A072769 * A322438 A304572 A070204

Adjacent sequences:  A322434 A322435 A322436 * A322438 A322439 A322440

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 08 2018

STATUS

approved

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Last modified July 12 21:31 EDT 2020. Contains 335669 sequences. (Running on oeis4.)