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 A322103 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{d|n} sigma_k(d). 3
 1, 1, 3, 1, 4, 3, 1, 6, 5, 6, 1, 10, 11, 11, 3, 1, 18, 29, 27, 7, 9, 1, 34, 83, 83, 27, 20, 3, 1, 66, 245, 291, 127, 66, 9, 10, 1, 130, 731, 1091, 627, 290, 51, 26, 6, 1, 258, 2189, 4227, 3127, 1494, 345, 112, 18, 9, 1, 514, 6563, 16643, 15627, 8330, 2403, 668, 102, 28, 3 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Seiichi Manyama, Antidiagonals n = 1..140, flattened FORMULA G.f. of column k: Sum_{j>=1} sigma_k(j)*x^j/(1 - x^j). A(n,k) = Sum_{d|n} d^k*tau(n/d). EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, ... 3, 4, 6, 10, 18, 34, ... 3, 5, 11, 29, 83, 245, ... 6, 11, 27, 83, 291, 1091, ... 3, 7, 27, 127, 627, 3127, ... 9, 20, 66, 290, 1494, 8330, ... MATHEMATICA Table[Function[k, Sum[DivisorSigma[k, d], {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten Table[Function[k, SeriesCoefficient[Sum[DivisorSigma[k, j] x^j/(1 - x^j), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten PROG (PARI) T(n, k)={sumdiv(n, d, d^k*numdiv(n/d))} for(n=1, 10, for(k=0, 8, print1(T(n, k), ", ")); print); \\ Andrew Howroyd, Nov 26 2018 CROSSREFS Columns k=0..3 give A007425, A007429, A007433, A321140. Cf. A109974, A321141 (diagonal), A356045. Sequence in context: A104568 A030758 A347065 * A272172 A104764 A152842 Adjacent sequences: A322100 A322101 A322102 * A322104 A322105 A322106 KEYWORD nonn,tabl AUTHOR Ilya Gutkovskiy, Nov 26 2018 STATUS approved

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Last modified December 1 14:09 EST 2023. Contains 367476 sequences. (Running on oeis4.)