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

1,30

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

See link for additional cross-references.

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

Sequence in context: A200627 A152889 A216273 * A376504 A151905 A226997

Adjacent sequences: A327514 A327515 A327516 * A327518 A327519 A327520

Keyword

nonn

Author

Gus Wiseman, Sep 19 2019

Status

approved