A333558 - OEIS

%I #11 May 09 2021 09:39:12

%S 2,5,12,19,46,41,104,95,150,165,312,203,494,365,432,519,946,545,1208,

%T 747,990,1105,1828,991,1986,1709,2004,1663,3054,1481,3812,2615,3062,

%U 3173,3724,2519,5654,4145,4512,3591,7162,3449,8024,4979,5298,6209,9708,4983,9638,6685

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

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

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

%F 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

%t Table[Sum[EulerPhi[d] Prime[d], {d, Divisors[n]}], {n, 1, 50}]

%t Table[Sum[Prime[n/GCD[n, k]], {k, 1, n}], {n, 1, 50}]

%o (PARI) a(n) = sumdiv(n, d, prime(d)*eulerphi(d)); \\ _Michel Marcus_, Mar 27 2020

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

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Mar 26 2020