A347134 a(n) = Sum_{d|n} phi(n/d) * A069359(d), where phi is Euler totient function.

0, 1, 1, 3, 1, 8, 1, 8, 5, 12, 1, 23, 1, 16, 14, 20, 1, 36, 1, 35, 18, 24, 1, 60, 9, 28, 21, 47, 1, 87, 1, 48, 26, 36, 22, 103, 1, 40, 30, 92, 1, 119, 1, 71, 66, 48, 1, 148, 13, 92, 38, 83, 1, 144, 30, 124, 42, 60, 1, 247, 1, 64, 86, 112, 34, 183, 1, 107, 50, 183, 1, 268, 1, 76, 110, 119, 34, 215, 1, 228, 81, 84

Offset: 1

Author

Antti Karttunen, Aug 23 2021

Keywords

• nonn

Comments

Dirichlet convolution of A000010 (Euler totient function phi) with A069359.

Dirichlet convolution of A001221 (omega) with A029935 (the convolution square of Euler phi).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000010, A001221, A069359, A029935.

Cf. also A347131, A347133, A347135.

Programs

Mathematica

Table[DivisorSum[n,EulerPhi[n/#]*#*DivisorSum[#,1/#&,PrimeQ]&],{n,82}] (* Giorgos Kalogeropoulos, Oct 28 2021 *)

PARI

A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359
A347134(n) = sumdiv(n,d,eulerphi(n/d)*A069359(d));

Formula

a(n) = Sum_{d|n} A000010(n/d) * A069359(d)

a(n) = Sum_{d|n} A001221(n/d) * A029935(d).

a(n) = Sum_{k=1..n} A069359(gcd(n,k)). - Antti Karttunen, Oct 17 2021