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A308674 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k).

%I A308674 #20 May 11 2021 01:54:17
%S A308674 1,1,3,1,5,4,1,17,28,7,1,257,19684,261,6,1,65537,7625597484988,
%T A308674 4294967313,3126,12,1,4294967297,
%U A308674 443426488243037769948249630619149892804,340282366920938463463374607431768211713,298023223876953126,46688,8
%N A308674 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k).
%H A308674 Seiichi Manyama, <a href="/A308674/b308674.txt">Antidiagonals n = 1..9, flattened</a>
%F A308674 L.g.f. of column k: -log(Product_{j>=1} (1 - x^j)^(j^(j^k-1))).
%e A308674 Square array begins:
%e A308674    1,   1,          1,                                       1, ...
%e A308674    3,   5,         17,                                     257, ...
%e A308674    4,  28,      19684,                           7625597484988, ...
%e A308674    7, 261, 4294967313, 340282366920938463463374607431768211713, ...
%t A308674 T[n_, k_] := DivisorSum[n, #^(#^k) &]; Table[T[k, n - k], {n, 1, 7}, {k, 1, n}] // Flatten (* _Amiram Eldar_, May 11 2021 *)
%Y A308674 Columns k=0..3 give A000203, A062796, A308671, A308672.
%Y A308674 Cf. A308676.
%K A308674 nonn,tabl
%O A308674 1,3
%A A308674 _Seiichi Manyama_, Jun 16 2019