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 A308690 Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{d|n} d^(k*n/d - k + 1), read by antidiagonals. 4
 1, 1, 3, 1, 3, 4, 1, 3, 4, 7, 1, 3, 4, 9, 6, 1, 3, 4, 13, 6, 12, 1, 3, 4, 21, 6, 24, 8, 1, 3, 4, 37, 6, 66, 8, 15, 1, 3, 4, 69, 6, 216, 8, 41, 13, 1, 3, 4, 133, 6, 762, 8, 201, 37, 18, 1, 3, 4, 261, 6, 2784, 8, 1289, 253, 68, 12, 1, 3, 4, 517, 6, 10386, 8, 9225, 2197, 648, 12, 28 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Seiichi Manyama, Antidiagonals n = 1..140, flattened FORMULA L.g.f. of column k: -log(Product_{j>=1} (1 - j^k*x^j)^(1/j^k)). A(p,k) = p+1 for prime p. EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, 1, ... 3, 3, 3, 3, 3, 3, 3, ... 4, 4, 4, 4, 4, 4, 4, ... 7, 9, 13, 21, 37, 69, 133, ... 6, 6, 6, 6, 6, 6, 6, ... 12, 24, 66, 216, 762, 2784, 10386, ... 8, 8, 8, 8, 8, 8, 8, ... MATHEMATICA T[n_, k_] := DivisorSum[n, #^(k*n/# - k + 1) &]; Table[T[k, n - k], {n, 1, 12}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *) CROSSREFS Columns k=0..3 give A000203, A055225, A308688, A308689. Cf. A294579, A308509, A308694. Sequence in context: A107638 A245093 A104765 * A329512 A064884 A093560 Adjacent sequences: A308687 A308688 A308689 * A308691 A308692 A308693 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Jun 17 2019 STATUS approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)