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A359112
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a(n) = Sum_{d|n} (n/d) * d^(n-d).
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8
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1, 3, 4, 13, 6, 109, 8, 777, 2197, 7541, 12, 374809, 14, 1675773, 31954096, 100794385, 18, 7391871271, 20, 163547770441, 2037381161992, 570634875581, 24, 1275177760626097, 476837158203151, 605750431288341, 450286447756825720, 2258377795760750777, 30
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} x^k/(1 - (k * x)^k)^2.
If p is prime, a(p) = 1 + p.
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MATHEMATICA
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a[n_] := DivisorSum[n, #^(n-#)*n/# &]; Array[a, 29] (* Amiram Eldar, Aug 27 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, n/d*d^(n-d));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k)^2))
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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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