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

1,4

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A001221, A069359, A029935.

Cf. also A347131, A347133, A347135.

Sequence in context: A347956 A280207 A319045 * A360705 A182510 A112420

Adjacent sequences: A347131 A347132 A347133 * A347135 A347136 A347137

Keyword

nonn

Author

Antti Karttunen, Aug 23 2021

Status

approved