A320777 - OEIS

%I #6 Oct 22 2018 17:42:49

%S 1,0,1,1,0,0,0,0,-1,-1,1,1,0,-1,0,1,-1,-2,1,3,1,-2,-2,1,0,-4,0,6,6,-4,

%T -8,1,4,-4,-5,10,16,-4,-25,-7,17,5,-16,2,42,12,-58,-48,40,59,-27,-44,

%U 67,86,-103,-187,36,236,45,-213,-5,284,-23,-526,-188,663,520

%N Inverse Euler transform of the number of distinct prime factors (without multiplicity) function A001221.

%C 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.

%t 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 Table[Sum[MoebiusMu[i/d]*final[[d]],{d,Divisors[i]}]/i,{i,Length[seq]}]];

%t EulerInvTransform[Array[PrimeNu,100]]

%Y Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054.

%Y Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549.

%Y Inverse Euler transforms: A059966, A320767, A320776, A320778, A320779, A320780, A320781, A320782.

%K sign

%O 0,18

%A _Gus Wiseman_, Oct 22 2018