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 A322104 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{d|n} d*sigma_k(d). 0
 1, 1, 5, 1, 7, 7, 1, 11, 13, 17, 1, 19, 31, 35, 11, 1, 35, 85, 95, 31, 35, 1, 67, 247, 311, 131, 91, 15, 1, 131, 733, 1127, 631, 341, 57, 49, 1, 259, 2191, 4295, 3131, 1615, 351, 155, 34, 1, 515, 6565, 16775, 15631, 8645, 2409, 775, 130, 55, 1, 1027, 19687, 66311, 78131, 49111, 16815, 4991, 850, 217, 23 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..66. FORMULA G.f. of column k: Sum_{j>=1} j*sigma_k(j)*x^j/(1 - x^j). L.g.f. of column k: -log(Product_{j>=1} (1 - x^j)^sigma_k(j)). A(n,k) = Sum_{d|n} d^(k+1)*sigma_1(n/d). EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, ... 5, 7, 11, 19, 35, 67, ... 7, 13, 31, 85, 247, 733, ... 17, 35, 95, 311, 1127, 4295, ... 11, 31, 131, 631, 3131, 15631, ... 35, 91, 341, 1615, 8645, 49111, ... MATHEMATICA Table[Function[k, Sum[d DivisorSigma[k, d], {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten Table[Function[k, SeriesCoefficient[Sum[j 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+1)*sigma(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 A060640, A001001, A027847, A027848. Cf. A109974, A320940 (diagonal), A321876, A322103. Sequence in context: A187561 A088515 A200638 * A100122 A001945 A342921 Adjacent sequences: A322101 A322102 A322103 * A322105 A322106 A322107 KEYWORD nonn,tabl AUTHOR Ilya Gutkovskiy, Nov 26 2018 STATUS approved

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Last modified November 28 22:38 EST 2023. Contains 367422 sequences. (Running on oeis4.)