A322436 Number of pairs of factorizations of n into factors > 1 where no factor of the second properly divides any factor of the first.

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

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