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 A322263 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = numerator of Sum_{d|n} 1/d^k. 1
 1, 1, 2, 1, 3, 2, 1, 5, 4, 3, 1, 9, 10, 7, 2, 1, 17, 28, 21, 6, 4, 1, 33, 82, 73, 26, 2, 2, 1, 65, 244, 273, 126, 25, 8, 4, 1, 129, 730, 1057, 626, 7, 50, 15, 3, 1, 257, 2188, 4161, 3126, 697, 344, 85, 13, 4, 1, 513, 6562, 16513, 15626, 671, 2402, 585, 91, 9, 2, 1, 1025, 19684, 65793, 78126, 23725, 16808, 4369, 757, 13, 12, 6 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA G.f. of column k: Sum_{j>=1} x^j/(j^k*(1 - x^j)) (for rationals Sum_{d|n} 1/d^k). Dirichlet g.f. of column k: zeta(s)*zeta(s+k) (for rationals Sum_{d|n} 1/d^k). A(n,k) = numerator of sigma_k(n)/n^k. EXAMPLE Square array begins:   1,    1,      1,        1,        1,          1,  ...   2,  3/2,    5/4,      9/8,    17/16,      33/32,  ...   2,  4/3,   10/9,    28/27,    82/81,    244/243,  ...   3,  7/4,  21/16,    73/64,  273/256,  1057/1024,  ...   2,  6/5,  26/25,  126/125,  626/625,  3126/3125,  ...   4,    2,  25/18,      7/6,  697/648,    671/648,  ... MATHEMATICA Table[Function[k, Numerator[DivisorSigma[-k, n]]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten Table[Function[k, Numerator[DivisorSigma[k, n]/n^k]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten Table[Function[k, Numerator[SeriesCoefficient[Sum[x^j/(j^k (1 - x^j)), {j, 1, n}], {x, 0, n}]]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten CROSSREFS Columns k=0..24 give A000005, A017665, A017667, A017669, A017671, A017673, A017675, A017677, A017679, A017681, A017683, A017685, A017687, A017689, A017691, A017693, A017695, A017697, A017699, A017701, A017703, A017705, A017707, A017709, A017711. Denominators are in A322264. Cf. A109974, A279394. Sequence in context: A058400 A131344 A129262 * A279394 A308509 A280514 Adjacent sequences:  A322260 A322261 A322262 * A322264 A322265 A322266 KEYWORD nonn,tabl,frac AUTHOR Ilya Gutkovskiy, Dec 01 2018 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)