A320732 Number of factorizations of n into primes or semiprimes.

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

Offset

1,4

Links

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

Example

The a(60) = 5 factorizations are (2*2*3*5), (2*2*15), (2*3*10), (2*5*6), (3*4*5), (4*15), (6*10).

Mathematica

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

Crossrefs

Cf. A001055, A001222, A001358, A007716, A007717, A037143, A045778, A320663, A320655.

Sequence in context: A327399 A122375 A038548 * A305149 A336737 A327400

Adjacent sequences: A320729 A320730 A320731 * A320733 A320734 A320735

Keyword

nonn

Author

Gus Wiseman, Oct 20 2018

Status

approved