A345281 - OEIS

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A345281

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

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

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..76.

EXAMPLE

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

MATHEMATICA

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

CROSSREFS