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A309368 a(n) = Sum_{d|n} prime(n/d)^d. 0
2, 7, 13, 32, 43, 129, 145, 405, 660, 1417, 2079, 5999, 8233, 18903, 37271, 74912, 131131, 300239, 524355, 1139985, 2180263, 4372491, 8388691, 17853809, 33715580, 68704969, 136183123, 274127445, 536871021, 1100025921, 2147483775, 4343912079, 8638792645, 17309012967, 34380645545 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..35.

FORMULA

G.f.: Sum_{k>=1} prime(k)*x^k/(1 - prime(k)*x^k).

L.g.f.: -log(Product_{k>=1} (1 - prime(k)*x^k)^(1/k)).

a(n) ~ 2^n.

MATHEMATICA

Table[Sum[Prime[n/d]^d, {d, Divisors[n]}], {n, 1, 35}]

nmax = 35; CoefficientList[Series[Sum[Prime[k] x^k/(1 - Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

nmax = 35; CoefficientList[Series[-Log[Product[(1 - Prime[k] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest

CROSSREFS

Cf. A000040, A007445, A055225.

Sequence in context: A231478 A320680 A079119 * A051748 A330452 A086904

Adjacent sequences:  A309365 A309366 A309367 * A309369 A309370 A309371

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 25 2019

STATUS

approved

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Last modified November 27 16:35 EST 2021. Contains 349394 sequences. (Running on oeis4.)