A308571
a(n) = sigma_{n^2}(n).
Original entry on oeis.org
1, 17, 19684, 4295032833, 298023223876953126, 10314424798640630250188424914, 256923577521058878088611477224235621321608, 6277101735386680764176071790128604879584176795969512275969
Offset: 1
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Table[DivisorSigma[n^2, n], {n, 1, 10}] (* Vaclav Kotesovec, Jun 08 2019 *)
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{a(n) = sigma(n, n^2)}
A308676
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k * n/d).
Original entry on oeis.org
1, 1, 3, 1, 5, 4, 1, 17, 28, 9, 1, 257, 19684, 273, 6, 1, 65537, 7625597484988, 4294967553, 3126, 24, 1, 4294967297, 443426488243037769948249630619149892804, 340282366920938463463374607431768276993, 298023223876953126, 47450, 8
Offset: 1
Square array begins:
1, 1, 1, 1, ...
3, 5, 17, 257, ...
4, 28, 19684, 7625597484988, ...
9, 273, 4294967553, 340282366920938463463374607431768276993, ...
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T[n_, k_] := DivisorSum[n, #^(n * #^(k-1)) &]; Table[T[k, n - k], {n, 1, 7}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *)
A308671
a(n) = Sum_{d|n} d^(d^2).
Original entry on oeis.org
1, 17, 19684, 4294967313, 298023223876953126, 10314424798490535546171968756, 256923577521058878088611477224235621321608, 6277101735386680763835789423207666416102355444468329480209
Offset: 1
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a[n_] := DivisorSum[n, #^(#^2) &]; Array[a, 8] (* Amiram Eldar, May 11 2021 *)
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{a(n) = sumdiv(n, d, d^d^2)}
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N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^(k^(k^2-1))))))
A308675
a(n) = Sum_{d|n} d^(d^2 * n).
Original entry on oeis.org
1, 257, 7625597484988, 340282366920938463463374607431768276993, 2350988701644575015937473074444491355637331113544175043017503412556834518909454345703126
Offset: 1
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Table[Total[#^(#^2 n)&/@Divisors[n]],{n,5}] (* Harvey P. Dale, Feb 29 2020 *)
a[n_] := DivisorSum[n, #^(n * #^2) &]; Array[a, 5] (* Amiram Eldar, May 11 2021 *)
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{a(n) = sumdiv(n, d, d^(d^2*n))}
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N=10; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k^k^2*x)^k)^(1/k)))))
Showing 1-4 of 4 results.
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