A356240
a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^n.
Original entry on oeis.org
0, 1, 9, 114, 1332, 25404, 395460, 9724901, 207584371, 6120938951, 151737244257, 5932533980409, 168400694345669, 7145593797561899, 260681076993636793, 12410128414690753548, 473029927456547840472, 27572016889372245275679
Offset: 1
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a[n_] := Sum[(k - 1)^n * Sum[j^n, {j, 1, Floor[n/k]}], {k, 1, n}]; Array[a, 18] (* Amiram Eldar, Jul 30 2022 *)
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a(n) = sum(k=1, n, (k-1)^n*sum(j=1, n\k, j^n));
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a(n) = sum(k=1, n, k^n*(sigma(k, 0)-(n\k)^n));
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a(n) = sum(k=1, n, k^n*sumdiv(k, d, (1-1/d)^n));
A356250
Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} (j * floor(n/j))^k.
Original entry on oeis.org
1, 1, 2, 1, 4, 3, 1, 8, 8, 4, 1, 16, 22, 15, 5, 1, 32, 62, 57, 21, 6, 1, 64, 178, 219, 91, 33, 7, 1, 128, 518, 849, 405, 185, 41, 8, 1, 256, 1522, 3315, 1843, 1053, 247, 56, 9, 1, 512, 4502, 13017, 8541, 6065, 1523, 402, 69, 10, 1, 1024, 13378, 51339, 40171, 35253, 9571, 2948, 545, 87, 11
Offset: 1
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
2, 4, 8, 16, 32, 64, 128, ...
3, 8, 22, 62, 178, 518, 1522, ...
4, 15, 57, 219, 849, 3315, 13017, ...
5, 21, 91, 405, 1843, 8541, 40171, ...
6, 33, 185, 1053, 6065, 35253, 206345, ...
7, 41, 247, 1523, 9571, 61091, 394987, ...
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T[n_, k_] := Sum[(j * Floor[n/j])^k, {j, 1, n}]; Table[T[k, n - k], {n, 1, 11}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 31 2022 *)
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T(n, k) = sum(j=1, n, (j*(n\j))^k);
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T(n, k) = if(k==0, n, sum(j=1, n, j^k*sumdiv(j, d, 1-(1-1/d)^k)));
Showing 1-2 of 2 results.