A294786 Number of ways to choose a set partition of a factorization of n into distinct factors greater than one such that different blocks have different products.

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, 11, 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, 9, 3, 12, 1, 5, 3, 12, 1, 26, 1, 3, 5, 5, 3, 12, 1, 19, 3, 3

Offset

1,6

Links

Michael De Vlieger, Table of n, a(n) for n = 1..16384

Formula

a(product of n distinct primes) = A000258(n).

a(prime^n) = A279375(n).

Example

The a(36)=11 ways are:
(2)*(3)*(6),
(2)*(3*6), (2*6)*(3), (2)*(18), (3)*(12), (4)*(9),
(2*3*6), (2*18), (3*12), (4*9), (36).

Mathematica

sfs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[sfs[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@@Function[fac, Select[sps[fac], UnsameQ@@Times@@@#&]]/@sfs[n]], {n, 100}]

Crossrefs

Cf. A000258, A001055, A045778, A279375, A281113, A294787, A294788.

Sequence in context: A233269 A035689 A296082 * A294787 A294788 A254578

Adjacent sequences: A294783 A294784 A294785 * A294787 A294788 A294789

Keyword

nonn

Author

Gus Wiseman, Nov 08 2017

Status

approved