A308698
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(k*d).
Original entry on oeis.org
1, 1, 2, 1, 5, 2, 1, 17, 28, 3, 1, 65, 730, 261, 2, 1, 257, 19684, 65553, 3126, 4, 1, 1025, 531442, 16777281, 9765626, 46688, 2, 1, 4097, 14348908, 4294967553, 30517578126, 2176783082, 823544, 4, 1, 16385, 387420490, 1099511628801, 95367431640626, 101559956688164, 678223072850, 16777477, 3
Offset: 1
Square array begins:
1, 1, 1, 1, 1, ...
2, 5, 17, 65, 257, ...
2, 28, 730, 19684, 531442, ...
3, 261, 65553, 16777281, 4294967553, ...
2, 3126, 9765626, 30517578126, 95367431640626, ...
-
T[n_, k_] := DivisorSum[n, #^(k*#) &]; Table[T[k, n - k], {n, 1, 9}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *)
A308753
a(n) = Sum_{d|n} d^(2*(d-1)).
Original entry on oeis.org
1, 5, 82, 4101, 390626, 60466262, 13841287202, 4398046515205, 1853020188851923, 1000000000000390630, 672749994932560009202, 552061438912436478063702, 542800770374370512771595362, 629983141281877223617054459942
Offset: 1
-
a[n_] := DivisorSum[n, #^(2*(# - 1)) &]; Array[a, 14] (* Amiram Eldar, May 08 2021 *)
-
{a(n) = sumdiv(n, d, d^(2*(d-1)))}
-
N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-3)))))
-
N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*(k-1))*x^k/(1-x^k)))
A308704
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(k*d+1).
Original entry on oeis.org
1, 1, 3, 1, 9, 4, 1, 33, 82, 7, 1, 129, 2188, 1033, 6, 1, 513, 59050, 262177, 15626, 12, 1, 2049, 1594324, 67108993, 48828126, 280026, 8, 1, 8193, 43046722, 17179869697, 152587890626, 13060696236, 5764802, 15, 1, 32769, 1162261468, 4398046513153, 476837158203126, 609359740069674, 4747561509944, 134218761, 13
Offset: 1
Square array begins:
1, 1, 1, 1, 1, ...
3, 9, 33, 129, 513, ...
4, 82, 2188, 59050, 1594324, ...
7, 1033, 262177, 67108993, 17179869697, ...
6, 15626, 48828126, 152587890626, 476837158203126, ...
-
T[n_, k_] := DivisorSum[n, #^(k*# + 1) &]; Table[T[k, n - k], {n, 1, 9}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *)
Showing 1-3 of 3 results.