A349620 Dirichlet convolution of A003415 with the Dirichlet inverse of A003958.

0, 1, 1, 3, 1, 2, 1, 8, 4, 2, 1, 5, 1, 2, 2, 20, 1, 7, 1, 5, 2, 2, 1, 12, 6, 2, 15, 5, 1, 3, 1, 48, 2, 2, 2, 17, 1, 2, 2, 12, 1, 3, 1, 5, 7, 2, 1, 28, 8, 11, 2, 5, 1, 24, 2, 12, 2, 2, 1, 7, 1, 2, 7, 112, 2, 3, 1, 5, 2, 3, 1, 40, 1, 2, 11, 5, 2, 3, 1, 28, 54, 2, 1, 7, 2, 2, 2, 12, 1, 10, 2, 5, 2, 2, 2, 64, 1, 15

Offset: 1

Author

Antti Karttunen, Nov 25 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A003415, A097945.

Cf. also A349133, A349394, A349618, A349619, A349621.

Programs

Mathematica

f[p_, e_] := e/p; d[1] = 0; d[n_] := n*Plus @@ f @@@ FactorInteger[n]; a[n_] := DivisorSum[n, MoebiusMu[#] * EulerPhi[#] * d[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 25 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A097945(n) = (moebius(n)*eulerphi(n)); \\ Also Dirichlet inverse of A003958.
A349620(n) = sumdiv(n,d,A003415(n/d)*A097945(d));

Formula

a(n) = Sum_{d|n} A003415(n/d) * A097945(d).