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A308502
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Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{d|n} d^(n/d + k).
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4
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1, 1, 3, 1, 5, 4, 1, 9, 10, 9, 1, 17, 28, 25, 6, 1, 33, 82, 81, 26, 24, 1, 65, 244, 289, 126, 80, 8, 1, 129, 730, 1089, 626, 330, 50, 41, 1, 257, 2188, 4225, 3126, 1604, 344, 161, 37, 1, 513, 6562, 16641, 15626, 8634, 2402, 833, 163, 68, 1, 1025, 19684, 66049, 78126, 49100, 16808, 5249, 973, 290, 12
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OFFSET
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1,3
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LINKS
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FORMULA
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L.g.f. of column k: -log(Product_{j>=1} (1 - j*x^j)^(j^(k-1))).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
3, 5, 9, 17, 33, 65, ...
4, 10, 28, 82, 244, 730, ...
9, 25, 81, 289, 1089, 4225, ...
6, 26, 126, 626, 3126, 15626, ...
24, 80, 330, 1604, 8634, 49100, ...
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MATHEMATICA
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T[n_, k_] := DivisorSum[n, #^(n/# + k) &]; Table[T[k, n - k], {n, 1, 11}, {k, 1, n}] // Flatten (* Amiram Eldar, May 11 2021 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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