A335079 Row sums of A335078.

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, 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, 4, 2, 6, 1, 24, 1, 2, 4, 4, 2, 6, 1, 16, 5, 2, 1, 16, 2, 2, 2, 8, 1, 16

Offset

2,3

Links

Stefano Spezia, Table of n, a(n) for n = 2..10000

Mathematica

tau[n_, k_]:=If[n==1, 1, Product[Binomial[Extract[Extract[FactorInteger[n], i], 2]+k, k], {i, 1, Length[FactorInteger[n]]}]]; (* A334997 *)
Nd[n_, m_]:=Sum[(-1)^k*Binomial[m, k]*tau[n, m-k-1], {k, 0, m-1}]; (* A334996 *)
T[n_, k_]:=1/k*DivisorSum[k, EulerPhi[#]*Nd[n^(1/#), k/#]&, IntegerQ[n^(1/#)]&]; (* A335078 *)
Table[Sum[T[n, m], {m, 1, PrimeOmega[n]}], {n, 2, 90}]

Prog

(PARI) TT(n, k) = if (k==0, 1, sumdiv(n, d, TT(d, k-1))); \\ A334996
U(n, m) = sum(k=0, m-1, (-1)^k*binomial(m, k)*TT(n, m-k-1));
T(n, k) = my(p); (1/k)*sumdiv(k, d, if (ispower(n, d, &p), eulerphi(d)*U(p, k/d)));
row(n) = vector(bigomega(n), k, T(n, k)); \\ A335078
a(n) = vecsum(row(n)); \\ Michel Marcus, May 25 2020

Crossrefs

Cf. A001222 (Omega function), A334996, A334997, A335078.

Sequence in context: A305254 A252665 A001055 * A337093 A320266 A277692

Adjacent sequences: A335076 A335077 A335078 * A335080 A335081 A335082

Keyword

nonn

Author

Stefano Spezia, May 23 2020

Status

approved