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A319278 Square array sigma_k(n) read down antidiagonals: sum of the k-th powers of the divisors of n.

%I A319278 #18 Mar 16 2025 11:30:17
%S A319278 1,1,3,1,5,4,1,9,10,7,1,17,28,21,6,1,33,82,73,26,12,1,65,244,273,126,
%T A319278 50,8,1,129,730,1057,626,252,50,15,1,257,2188,4161,3126,1394,344,85,
%U A319278 13,1,513,6562,16513,15626,8052,2402,585,91,18,1,1025,19684,65793,78126,47450,16808,4369,757,130,12
%N A319278 Square array sigma_k(n) read down antidiagonals: sum of the k-th powers of the divisors of n.
%C A319278 Equals the square array A082771 without its first column.
%F A319278 sigma_k(n) = sum_{d|n} d^k.
%e A319278 The array starts in row n=1 with columns k>=1 as:
%e A319278      1      1      1      1      1      1       1        1
%e A319278      3      5      9     17     33     65     129      257
%e A319278      4     10     28     82    244    730    2188     6562
%e A319278      7     21     73    273   1057   4161   16513    65793
%e A319278      6     26    126    626   3126  15626   78126   390626
%e A319278     12     50    252   1394   8052  47450  282252  1686434
%e A319278      8     50    344   2402  16808 117650  823544  5764802
%e A319278     15     85    585   4369  33825 266305 2113665 16843009
%t A319278 T[n_, k_] := DivisorSigma[k, n];
%t A319278 Table[T[n-k+1, k], {n, 1, 11}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Dec 16 2021 *)
%Y A319278 Columns: A000203, A001157, A001158, A001159.
%Y A319278 Rows: A000012, A000051, A034472, A001576, A034474, A034488.
%Y A319278 Cf. A082771, A023887 (diagonal), A109974, A319194 (partial column sums).
%K A319278 nonn,tabl,easy
%O A319278 1,3
%A A319278 _R. J. Mathar_, Sep 16 2018