A349619 Dirichlet convolution of A003415 with the Dirichlet inverse of A003557.

0, 1, 1, 3, 1, 3, 1, 7, 5, 5, 1, 7, 1, 7, 6, 15, 1, 9, 1, 13, 8, 11, 1, 15, 9, 13, 19, 19, 1, 14, 1, 31, 12, 17, 10, 17, 1, 19, 14, 29, 1, 20, 1, 31, 24, 23, 1, 31, 13, 25, 18, 37, 1, 27, 14, 43, 20, 29, 1, 30, 1, 31, 34, 63, 16, 32, 1, 49, 24, 34, 1, 33, 1, 37, 34, 55, 16, 38, 1, 61, 65, 41, 1, 44, 20, 43, 30, 71

Offset

1,4

Links

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

Formula

a(n) = Sum_{d|n} A003415(n/d) * A349340(d).

Mathematica

f1[p_, e_] := e/p; d[1] = 0; d[n_] := n*Plus @@ f1 @@@ FactorInteger[n]; f[p_, e_] := -(p - 1)^(e - 1); s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := DivisorSum[n, s[#]*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]));
A349340(n) = { my(f=factor(n)); prod(i=1, #f~, -((f[i, 1]-1)^(f[i, 2]-1))); };
A349619(n) = sumdiv(n, d, A003415(n/d)*A349340(d));

Crossrefs

Cf. A003415, A003557, A349340.

Cf. also A349394, A349618, A349620, A349621.

Sequence in context: A322382 A122410 A309790 * A082495 A329385 A200476

Adjacent sequences: A349616 A349617 A349618 * A349620 A349621 A349622

Keyword

nonn

Author

Antti Karttunen, Nov 25 2021

Status

approved