A308670
a(n) = Sum_{d|n} d^(d*n).
Original entry on oeis.org
1, 17, 19684, 4294967553, 298023223876953126, 10314424798490535546559373642, 256923577521058878088611477224235621321608, 6277101735386680763835789423207666416120802188537744130049
Offset: 1
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a[n_] := DivisorSum[n, #^(#*n) &]; Array[a, 8] (* Amiram Eldar, May 11 2021 *)
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{a(n) = sumdiv(n, d, d^(d*n))}
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N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k^k*x)^k)^(1/k)))))
A308569
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(k*n).
Original entry on oeis.org
1, 1, 2, 1, 5, 2, 1, 17, 28, 3, 1, 65, 730, 273, 2, 1, 257, 19684, 65793, 3126, 4, 1, 1025, 531442, 16781313, 9765626, 47450, 2, 1, 4097, 14348908, 4295032833, 30517578126, 2177317874, 823544, 4, 1, 16385, 387420490, 1099512676353, 95367431640626, 101560344351050, 678223072850, 16843009, 3
Offset: 1
Square array begins:
1, 1, 1, 1, 1, ...
2, 5, 17, 65, 257, ...
2, 28, 730, 19684, 531442, ...
3, 273, 65793, 16781313, 4295032833, ...
2, 3126, 9765626, 30517578126, 95367431640626, ...
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T[n_, k_] := DivisorSum[n, #^(k*n) &]; Table[T[k, n - k], {n, 1, 9}, {k, 1, n}] // Flatten (* Amiram Eldar, May 11 2021 *)
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T(n,k) = sumdiv(n, d, d^(k*n));
matrix(5, 5, n, k, T(n,k-1)) \\ Michel Marcus, Jun 08 2019
A308593
a(n) = Sum_{d|n} d^(n^2/d).
Original entry on oeis.org
1, 5, 28, 513, 3126, 840242, 823544, 8606711809, 7625984905477, 1221277338483250, 285311670612, 89215914432866222355906, 302875106592254, 316913110043605007120962336162, 608295209422788113565012727970423808, 680564733921105089459460296530789924865
Offset: 1
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Table[Sum[d^(n^2/d), {d, Divisors[n]}], {n,1,20}] (* Vaclav Kotesovec, Jun 09 2019 *)
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{a(n) = sumdiv(n, d, d^(n^2/d))}
Showing 1-3 of 3 results.