A327517 - OEIS

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A327517

Number of factorizations of n that are empty or have at least two factors, all of which are > 1 and pairwise coprime.

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 4, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 4, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 4, 0, 1, 1, 0, 1, 4, 0, 1, 1, 4, 0, 1, 0, 1, 1, 1, 1, 4, 0, 1, 0, 1, 0, 4, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,30

LINKS

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

Gus Wiseman, Sequences counting and encoding certain classes of multisets

FORMULA

a(n > 1) = A259936(n) - 1 = A000110(A001221(n)) - 1.

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], #=={}||CoprimeQ@@#&]], {n, 100}]

CROSSREFS