A320732 - OEIS

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

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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.