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

Offset: 1

Author

Gus Wiseman, Sep 19 2019

Keywords

• nonn

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Cf. A302569, A302696, A304711, A305079, A327076, A327392.

Programs

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}]

Formula

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