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A308701
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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*(d-1)).
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4
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1, 1, 2, 1, 3, 2, 1, 5, 10, 3, 1, 9, 82, 67, 2, 1, 17, 730, 4101, 626, 4, 1, 33, 6562, 262153, 390626, 7788, 2, 1, 65, 59050, 16777233, 244140626, 60466262, 117650, 4, 1, 129, 531442, 1073741857, 152587890626, 470184985314, 13841287202, 2097219, 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 - x^j)^(j^(k*j-k-1))).
G.f. of column k: Sum_{j>=1} j^(k*(j-1)) * x^j/(1 - x^j).
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, ...
2, 3, 5, 9, 17, ...
2, 10, 82, 730, 6562, ...
3, 67, 4101, 262153, 16777233, ...
2, 626, 390626, 244140626, 152587890626, ...
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MATHEMATICA
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T[n_, k_] := DivisorSum[n, #^(k*(# - 1)) &]; Table[T[k, n - k], {n, 1, 9}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 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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