A345310 - OEIS

%I #5 Jun 28 2021 17:38:44

%S 0,2,3,4,5,5,7,4,27,7,11,7,13,9,8,4,17,29,19,9,10,13,23,7,3125,15,27,

%T 11,29,10,31,4,14,19,12,31,37,21,16,9,41,12,43,15,32,25,47,7,823543,

%U 3127,20,17,53,29,16,11,22,31,59,12,61,33,34,4,18,16,67,21,26,14,71,31

%N a(n) = Sum_{p|n, p prime} p^gcd(p,n/p).

%C a(p) = Sum_{p|p} p^gcd(p,p/p) = p^1 = p, for p prime.

%e a(18) = Sum_{p|18} p^gcd(p,18/p) = 2^gcd(2,9) + 3^gcd(3,6) = 2^1 + 3^3 = 29.

%t Table[Sum[k^GCD[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 13 2021