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A309368
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a(n) = Sum_{d|n} prime(n/d)^d.
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0
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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.
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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