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A338694
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a(n) = Sum_{d|n} d^d * binomial(d, n/d).
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5
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1, 8, 81, 1028, 15625, 280017, 5764801, 134219264, 3486784428, 100000031250, 3138428376721, 106993206079936, 3937376385699289, 155568095575106627, 6568408355712921875, 295147905179822588160, 14063084452067724991009, 708235345355351624428356, 37589973457545958193355601
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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} ( (k + k * x^k)^k - k^k ) = Sum_{k>=1} k^k * ( (1 + x^k)^k - 1 ).
If p is prime, a(p) = p^(p+1).
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MATHEMATICA
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a[n_] := DivisorSum[n, #^# * Binomial[#, n/#] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, d^d*binomial(d, n/d));
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, (k+k*x^k)^k-k^k))
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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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