A326514 Number of factorizations of n into factors > 1 where each factor has a different number of prime factors counted with multiplicity.

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

Offset

1,8

Links

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

Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Example

The a(96) = 8 factorizations: (2*4*12), (2*6*8), (2*48), (3*4*8), (3*32), (4*24), (6*16), (96).

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], UnsameQ@@PrimeOmega/@#&]], {n, 100}]

Crossrefs

Cf. A001055, A007837, A038041, A321455, A321469, A322794, A326026, A326515, A326516, A326517, A326533.

Sequence in context: A369167 A160267 A115621 * A077565 A316979 A331024

Adjacent sequences: A326511 A326512 A326513 * A326515 A326516 A326517

Keyword

nonn

Author

Gus Wiseman, Jul 11 2019

Status

approved