A326622 Number of factorizations of n into factors > 1 with integer average.

1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 2, 4, 1, 1, 1, 3, 2, 1, 1, 4, 2, 1, 3, 2, 1, 1, 1, 5, 2, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 3, 3, 1, 1, 6, 2, 2, 2, 2, 1, 2, 2, 4, 2, 1, 1, 6, 1, 1, 3, 7, 2, 1, 1, 3, 2, 1, 1, 6, 1, 1, 3, 2, 2, 2, 1, 7, 5, 1, 1, 4, 2, 1, 2, 3

Offset

1,3

Links

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

Example

The a(80) = 7 factorizations:
  (2*2*2*10)
  (2*2*20)
  (2*5*8)
  (2*40)
  (4*20)
  (8*10)
  (80)

Mathematica

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[n], IntegerQ[Mean[#]]&]], {n, 2, 100}]

Crossrefs

Partitions with integer average are A067538.

Strict partitions with integer average are A102627.

Heinz numbers of partitions with integer average are A316413.

Factorizations with integer geometric mean are A326028.

Cf. A001055, A051293, A078174, A078175, A326514, A326515, A326567/A326568, A326621, A326623.

Sequence in context: A305193 A038538 A293515 * A292777 A088529 A267116

Adjacent sequences: A326619 A326620 A326621 * A326623 A326624 A326625

Keyword

nonn

Author

Gus Wiseman, Jul 14 2019

Status

approved