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A308704
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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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3
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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
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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))).
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, ...
3, 9, 33, 129, 513, ...
4, 82, 2188, 59050, 1594324, ...
7, 1033, 262177, 67108993, 17179869697, ...
6, 15626, 48828126, 152587890626, 476837158203126, ...
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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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