A345283 - OEIS

%I #5 Jun 28 2021 17:37:00

%S 0,4,9,8,25,59,49,32,243,253,121,371,169,2391,5312,2048,289,4235,361,

%T 5173,193954,9523,529,185339,78125,133269,177147,147879,841,386344,

%U 961,131072,1755374,529201,49651668,2118611,1369,8395467,129511456,57216733,1681,138352314,1849

%N a(n) = Sum_{p|n, p prime} p^nextprime(n/p), where nextprime(n) is the smallest prime > n.

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

%e a(12) = Sum_{p|12} p^nextprime(12/p) = 2^7 + 3^5 = 371.

%t Table[Sum[k^NextPrime[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 60}]

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

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 12 2021