cp's OEIS Frontend

A335079 Row sums of A335078.

%I A335079 #11 May 29 2020 02:24:35
%S A335079 1,1,2,1,2,1,3,2,2,1,4,1,2,2,5,1,4,1,4,2,2,1,8,2,2,3,4,1,6,1,7,2,2,2,
%T A335079 11,1,2,2,8,1,6,1,4,4,2,1,16,2,4,2,4,1,8,2,8,2,2,1,16,1,2,4,13,2,6,1,
%U A335079 4,2,6,1,24,1,2,4,4,2,6,1,16,5,2,1,16,2,2,2,8,1,16
%N A335079 Row sums of A335078.
%H A335079 Stefano Spezia, <a href="/A335079/b335079.txt">Table of n, a(n) for n = 2..10000</a>
%t A335079 tau[n_,k_]:=If[n==1,1,Product[Binomial[Extract[Extract[FactorInteger[n],i],2]+k,k],{i,1,Length[FactorInteger[n]]}]]; (* A334997 *)
%t A335079 Nd[n_, m_]:=Sum[(-1)^k*Binomial[m, k]*tau[n, m-k-1], {k, 0, m-1}]; (* A334996 *)
%t A335079 T[n_,k_]:=1/k*DivisorSum[k,EulerPhi[#]*Nd[n^(1/#),k/#]&,IntegerQ[n^(1/#)]&]; (* A335078 *)
%t A335079 Table[Sum[T[n,m],{m,1,PrimeOmega[n]}],{n,2,90}]
%o A335079 (PARI) TT(n, k) = if (k==0, 1, sumdiv(n, d, TT(d, k-1))); \\ A334996
%o A335079 U(n, m) = sum(k=0, m-1, (-1)^k*binomial(m, k)*TT(n, m-k-1));
%o A335079 T(n, k) = my(p); (1/k)*sumdiv(k, d, if (ispower(n, d, &p), eulerphi(d)*U(p, k/d)));
%o A335079 row(n) = vector(bigomega(n), k, T(n,k)); \\ A335078
%o A335079 a(n) = vecsum(row(n)); \\ _Michel Marcus_, May 25 2020
%Y A335079 Cf. A001222 (Omega function), A334996, A334997, A335078.
%K A335079 nonn
%O A335079 2,3
%A A335079 _Stefano Spezia_, May 23 2020