cp's OEIS Frontend

A320785 Inverse Euler transform of the number of factorizations function A001055.

%I A320785 #4 Oct 22 2018 22:55:27
%S A320785 1,1,0,0,1,-1,1,-1,1,0,-1,1,-1,0,0,1,1,-3,3,-3,0,4,-6,6,-5,5,-1,-7,13,
%T A320785 -16,15,-8,-3,12,-25,41,-40,21,10,-51,83,-93,81,-38,-44,148,-234,258,
%U A320785 -190,35,184,-429,616,-660,480,-18,-640,1289,-1714,1693,-1039,-268
%N A320785 Inverse Euler transform of the number of factorizations function A001055.
%C A320785 The Euler transform of a sequence q is the sequence of coefficients of x^n, n > 0, in the expansion of Product_{n > 0} 1/(1 - x^n)^q(n). The constant term 1 is sometimes taken to be the zeroth part of the Euler transform.
%H A320785 OEIS Wiki, <a href="https://oeis.org/wiki/Euler_transform">Euler transform</a>
%t A320785 EulerInvTransform[{}]={};EulerInvTransform[seq_]:=Module[{final={}},For[i=1,i<=Length[seq],i++,AppendTo[final,i*seq[[i]]-Sum[final[[d]]*seq[[i-d]],{d,i-1}]]];
%t A320785 Table[Sum[MoebiusMu[i/d]*final[[d]],{d,Divisors[i]}]/i,{i,Length[seq]}]];
%t A320785 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A320785 EulerInvTransform[Table[Length[facs[n]],{n,100}]]
%Y A320785 Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054.
%Y A320785 Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549.
%Y A320785 Inverse Euler transforms: A059966, A320767, A320776, A320777, A320778, A320779, A320780, A320781, A320782.
%K A320785 sign
%O A320785 0,18
%A A320785 _Gus Wiseman_, Oct 22 2018