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A345283 a(n) = Sum_{p|n, p prime} p^nextprime(n/p), where nextprime(n) is the smallest prime > n. 0
0, 4, 9, 8, 25, 59, 49, 32, 243, 253, 121, 371, 169, 2391, 5312, 2048, 289, 4235, 361, 5173, 193954, 9523, 529, 185339, 78125, 133269, 177147, 147879, 841, 386344, 961, 131072, 1755374, 529201, 49651668, 2118611, 1369, 8395467, 129511456, 57216733, 1681, 138352314, 1849 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..43.

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A304203 A087687 A264090 * A297439 A168175 A164382

Adjacent sequences:  A345280 A345281 A345282 * A345284 A345285 A345286

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 12 2021

STATUS

approved

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Last modified May 20 05:39 EDT 2022. Contains 353851 sequences. (Running on oeis4.)