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%I #37 May 09 2021 02:50:40
%S 1,1,2,1,3,2,1,5,10,3,1,9,82,67,2,1,17,730,4101,626,4,1,33,6562,
%T 262153,390626,7788,2,1,65,59050,16777233,244140626,60466262,117650,4,
%U 1,129,531442,1073741857,152587890626,470184985314,13841287202,2097219,3
%N Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(k*(d-1)).
%H Seiichi Manyama, <a href="/A308701/b308701.txt">Antidiagonals n = 1..53, flattened</a>
%F L.g.f. of column k: -log(Product_{j>=1} (1 - x^j)^(j^(k*j-k-1))).
%F G.f. of column k: Sum_{j>=1} j^(k*(j-1)) * x^j/(1 - x^j).
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 2, 3, 5, 9, 17, ...
%e 2, 10, 82, 730, 6562, ...
%e 3, 67, 4101, 262153, 16777233, ...
%e 2, 626, 390626, 244140626, 152587890626, ...
%t T[n_, k_] := DivisorSum[n, #^(k*(# - 1)) &]; Table[T[k, n - k], {n, 1, 9}, {k, 1, n}] // Flatten (* _Amiram Eldar_, May 09 2021 *)
%Y Columns k=0..2 give A000005, A262843, A308753.
%Y Row n=1..3 give A000012, A000051, A062396.
%Y Cf. A308694, A308698, A308704.
%K nonn,tabl
%O 1,3
%A _Seiichi Manyama_, Jun 22 2019