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

1,4

Links

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

Formula

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

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 *)

Prog

(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));

Crossrefs

Cf. A003415, A097945.

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

Sequence in context: A322034 A351436 A226629 * A349380 A351425 A249580

Adjacent sequences: A349617 A349618 A349619 * A349621 A349622 A349623

Keyword

nonn

Author

Antti Karttunen, Nov 25 2021

Status

approved