A342677
a(n) = Sum_{d|n} (n/d)^(n-d+1).
Original entry on oeis.org
1, 5, 28, 265, 3126, 46916, 823544, 16793633, 387422677, 10001953190, 285311670612, 8916464313700, 302875106592254, 11112103714568680, 437893891601739648, 18446779258148749825, 827240261886336764178, 39346424755299348744797, 1978419655660313589123980
Offset: 1
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a[n_] := DivisorSum[n, (n/#)^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Mar 18 2021 *)
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a(n) = sumdiv(n, d, (n/d)^(n-d+1));
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k^(k-1)*x^k)))
A356539
a(n) = Sum_{d|n} d * 3^(n-d).
Original entry on oeis.org
1, 5, 12, 49, 86, 492, 736, 3977, 8757, 34030, 59060, 384924, 531454, 2672528, 6672552, 26093113, 43046738, 261646137, 387420508, 2181624374, 4682526672, 17435870644, 31381059632, 204908769276, 299863458511, 1412168408630, 3392641222200, 13912336721584
Offset: 1
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a[n_] := DivisorSum[n, # * 3^(n - #) &]; Array[a, 30] (* Amiram Eldar, Aug 11 2022 *)
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a(n) = sumdiv(n, d, d*3^(n-d));
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my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-(3*x)^k)))
A356529
a(n) = (n-1)! * Sum_{d|n} d^(n-d+1).
Original entry on oeis.org
1, 3, 8, 78, 144, 14400, 5760, 5851440, 88583040, 5859786240, 43545600, 24077414592000, 6706022400, 35948640894566400, 4395744249613516800, 263312496059348736000, 376610217984000, 5901087844517892009984000, 128047474114560000
Offset: 1
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a[n_] := (n - 1)! * DivisorSum[n, #^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Aug 10 2022 *)
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a(n) = (n-1)!*sumdiv(n, d, d^(n-d+1));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-(k*x)^k)/k^k)))
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