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A295632 Write 1/Product_{n > 1}(1 - 1/n^s) in the form Product_{n > 1}(1 + a(n)/n^s). 5

%I

%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,

%T 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,

%U 1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1

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

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

%t nn=100;

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t 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]]

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

%K sign

%O 2,3

%A _Gus Wiseman_, Nov 24 2017

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)