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)))))
A308674
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k).
Original entry on oeis.org
1, 1, 3, 1, 5, 4, 1, 17, 28, 7, 1, 257, 19684, 261, 6, 1, 65537, 7625597484988, 4294967313, 3126, 12, 1, 4294967297, 443426488243037769948249630619149892804, 340282366920938463463374607431768211713, 298023223876953126, 46688, 8
Offset: 1
Square array begins:
1, 1, 1, 1, ...
3, 5, 17, 257, ...
4, 28, 19684, 7625597484988, ...
7, 261, 4294967313, 340282366920938463463374607431768211713, ...
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T[n_, k_] := DivisorSum[n, #^(#^k) &]; Table[T[k, n - k], {n, 1, 7}, {k, 1, n}] // Flatten (* Amiram Eldar, May 11 2021 *)
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 1-3 of 3 results.
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