A294787 Number of ways to choose a set partition of a factorization of n into distinct factors greater than one.

1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 5, 1, 3, 3, 3, 1, 5, 1, 5, 3, 3, 1, 12, 1, 3, 3, 5, 1, 12, 1, 5, 3, 3, 3, 12, 1, 3, 3, 12, 1, 12, 1, 5, 5, 3, 1, 19, 1, 5, 3, 5, 1, 12, 3, 12, 3, 3, 1, 26, 1, 3, 5, 10, 3, 12, 1, 5, 3, 12, 1, 26, 1, 3, 5, 5, 3, 12, 1, 19, 3, 3

Offset

1,6

Links

Table of n, a(n) for n=1..82.

Formula

A294786(n) <= a(n) <= A294788(n).

Mathematica

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

Crossrefs

Cf. A001055, A045778, A279375, A281113, A294617, A294786, A294788.

Sequence in context: A035689 A296082 A294786 * A294788 A254578 A348610

Adjacent sequences: A294784 A294785 A294786 * A294788 A294789 A294790

Keyword

nonn

Author

Gus Wiseman, Nov 08 2017

Status

approved