A320889 Number of set partitions of strict factorizations of n into factors > 1 such that all the blocks have the same product.

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 5, 1, 2, 2, 3, 1, 5, 1, 3, 2, 2, 2, 6, 1, 2, 2, 5, 1, 5, 1, 3, 3, 2, 1, 7, 1, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 9, 1, 2, 3, 5, 2, 5, 1, 3, 2, 5, 1, 9, 1, 2, 3, 3, 2, 5, 1, 7, 2, 2, 1, 9, 2, 2, 2

Offset

1,6

Links

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

Example

The a(144) = 17 set partitions:
  (2*3*4*6)    (2*8*9)     (2*72)  (144)
  (2*6)*(3*4)  (3*6*8)     (3*48)
               (2*3*24)    (4*36)
               (2*4*18)    (6*24)
               (2*6*12)    (8*18)
               (3*4*12)    (9*16)
               (2*6)*(12)
               (3*4)*(12)

Mathematica

strfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strfacs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Join@@Table[Select[sps[fac], SameQ@@Times@@@#&], {fac, strfacs[n]}]], {n, 100}]

Crossrefs

Cf. A000110, A001055, A001970, A045778, A050336, A279375, A294786, A294787, A296132, A320886, A320887, A320888.

Sequence in context: A318357 A323091 A045778 * A296133 A338649 A337176

Adjacent sequences: A320886 A320887 A320888 * A320890 A320891 A320892

Keyword

nonn

Author

Gus Wiseman, Oct 23 2018

Status

approved