A333558 a(n) = Sum_{d|n} phi(d) * prime(d).

2, 5, 12, 19, 46, 41, 104, 95, 150, 165, 312, 203, 494, 365, 432, 519, 946, 545, 1208, 747, 990, 1105, 1828, 991, 1986, 1709, 2004, 1663, 3054, 1481, 3812, 2615, 3062, 3173, 3724, 2519, 5654, 4145, 4512, 3591, 7162, 3449, 8024, 4979, 5298, 6209, 9708, 4983, 9638, 6685

Offset: 1

Author

Ilya Gutkovskiy, Mar 26 2020

Keywords

• nonn

Crossrefs

Cf. A000010, A000040, A007445, A057660, A061150, A130029.

Programs

Mathematica

Table[Sum[EulerPhi[d] Prime[d], {d, Divisors[n]}], {n, 1, 50}]
Table[Sum[Prime[n/GCD[n, k]], {k, 1, n}], {n, 1, 50}]

PARI

a(n) = sumdiv(n, d, prime(d)*eulerphi(d)); \\ Michel Marcus, Mar 27 2020

Formula

G.f.: Sum_{k>=1} phi(k) * prime(k) * x^k / (1 - x^k).

a(n) = Sum_{k=1..n} prime(n/gcd(n,k)).

a(n) = Sum_{k=1..n} prime(gcd(n,k))*phi(gcd(n,k))/phi(n/gcd(n,k)). - Richard L. Ollerton, May 09 2021