A345282 - OEIS

%I #5 Jun 28 2021 17:36:41

%S 0,4,6,6,10,19,14,10,15,29,22,29,26,43,46,22,34,43,38,47,68,59,46,59,

%T 35,73,33,69,58,102,62,34,94,89,104,77,74,103,116,101,82,146,86,101,

%U 106,127,94,109,77,113,142,123,106,115,142,135,164,149,118,196,122,167,146,74,176

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

%C If p is prime, a(p) = Sum_{p|p} p * nextprime(p/p) = 2*p.

%e a(12) = Sum_{p|12} p * nextprime(12/p) = 2*7 + 3*5 = 14 + 15 = 29.

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

%Y Cf. A151800 (nextprime v.2), A345280, A345281.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 12 2021