A295632 Write 1/Product_{n > 1}(1 - 1/n^s) in the form Product_{n > 1}(1 + a(n)/n^s).

1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1

Offset

2,3

Comments

First negative entry is a(1024) = -4.

Links

Table of n, a(n) for n=2..88.

Mathematica

nn=100;
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Solve[Table[Length[facs[n]]==Sum[Times@@a/@f, {f, Select[facs[n], UnsameQ@@#&]}], {n, 2, nn}], Table[a[n], {n, 2, nn}]][[1, All, 2]]

Crossrefs

Cf. A001055, A045778, A050376, A220418, A220420, A273866, A273873, A289501, A290261, A290262, A290971, A290973, A295279, A295635, A295636.

Sequence in context: A275215 A304886 A352080 * A139549 A216915 A280569

Adjacent sequences: A295629 A295630 A295631 * A295633 A295634 A295635

Keyword

sign

Author

Gus Wiseman, Nov 24 2017

Status

approved