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%I #12 Jul 26 2022 10:09:38
%S 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,
%T 66,245,291,127,66,9,10,1,130,731,1091,627,290,51,26,6,1,258,2189,
%U 4227,3127,1494,345,112,18,9,1,514,6563,16643,15627,8330,2403,668,102,28,3
%N Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{d|n} sigma_k(d).
%H Seiichi Manyama, <a href="/A322103/b322103.txt">Antidiagonals n = 1..140, flattened</a>
%F G.f. of column k: Sum_{j>=1} sigma_k(j)*x^j/(1 - x^j).
%F A(n,k) = Sum_{d|n} d^k*tau(n/d).
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 3, 4, 6, 10, 18, 34, ...
%e 3, 5, 11, 29, 83, 245, ...
%e 6, 11, 27, 83, 291, 1091, ...
%e 3, 7, 27, 127, 627, 3127, ...
%e 9, 20, 66, 290, 1494, 8330, ...
%t Table[Function[k, Sum[DivisorSigma[k, d], {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
%t 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
%o (PARI) T(n,k)={sumdiv(n, d, d^k*numdiv(n/d))}
%o for(n=1, 10, for(k=0, 8, print1(T(n, k), ", ")); print); \\ _Andrew Howroyd_, Nov 26 2018
%Y Columns k=0..3 give A007425, A007429, A007433, A321140.
%Y Cf. A109974, A321141 (diagonal), A356045.
%K nonn,tabl
%O 1,3
%A _Ilya Gutkovskiy_, Nov 26 2018
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