A345281 - OEIS

%I #7 Jun 13 2021 15:32:20

%S 0,2,2,3,2,8,2,5,5,10,2,12,2,14,12,11,2,18,2,16,16,16,2,24,7,20,11,22,

%T 2,35,2,17,18,22,18,32,2,26,22,34,2,47,2,28,28,32,2,46,11,40,24,34,2,

%U 48,20,40,28,34,2,67,2,40,34,37,24,67,2,42,34,65,2,66,2,44,46,46

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

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

%e a(20) = Sum_{p|20} nextprime(20/p) = nextprime(10) + nextprime(4) = 11 + 5 = 16.

%t Table[Sum[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.

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Jun 12 2021