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A308569
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Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(k*n).
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3
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1, 1, 2, 1, 5, 2, 1, 17, 28, 3, 1, 65, 730, 273, 2, 1, 257, 19684, 65793, 3126, 4, 1, 1025, 531442, 16781313, 9765626, 47450, 2, 1, 4097, 14348908, 4295032833, 30517578126, 2177317874, 823544, 4, 1, 16385, 387420490, 1099512676353, 95367431640626, 101560344351050, 678223072850, 16843009, 3
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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^k*x)^j)^(1/j)).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, ...
2, 5, 17, 65, 257, ...
2, 28, 730, 19684, 531442, ...
3, 273, 65793, 16781313, 4295032833, ...
2, 3126, 9765626, 30517578126, 95367431640626, ...
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MATHEMATICA
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T[n_, k_] := DivisorSum[n, #^(k*n) &]; Table[T[k, n - k], {n, 1, 9}, {k, 1, n}] // Flatten (* Amiram Eldar, May 11 2021 *)
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PROG
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(PARI) T(n, k) = sumdiv(n, d, d^(k*n));
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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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