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A308676 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k * n/d).

%I A308676 #18 May 09 2021 02:51:18
%S A308676 1,1,3,1,5,4,1,17,28,9,1,257,19684,273,6,1,65537,7625597484988,
%T A308676 4294967553,3126,24,1,4294967297,
%U A308676 443426488243037769948249630619149892804,340282366920938463463374607431768276993,298023223876953126,47450,8
%N A308676 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k * n/d).
%H A308676 Seiichi Manyama, <a href="/A308676/b308676.txt">Antidiagonals n = 1..9, flattened</a>
%F A308676 L.g.f. of column k: -log(Product_{j>=1} (1 - j^(j^k) * x^j)^(1/j)).
%e A308676 Square array begins:
%e A308676    1,    1,          1,                                       1, ...
%e A308676    3,    5,         17,                                     257, ...
%e A308676    4,   28,      19684,                           7625597484988, ...
%e A308676    9,  273, 4294967553, 340282366920938463463374607431768276993, ...
%t A308676 T[n_, k_] := DivisorSum[n, #^(n * #^(k-1)) &]; Table[T[k, n - k], {n, 1, 7}, {k, 1, n}] // Flatten (* _Amiram Eldar_, May 09 2021 *)
%Y A308676 Columns k=0..3 give A055225, A023887, A308670, A308675.
%Y A308676 Cf. A308674.
%K A308676 nonn,tabl
%O A308676 1,3
%A A308676 _Seiichi Manyama_, Jun 16 2019