A308674 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k).
1, 1, 3, 1, 5, 4, 1, 17, 28, 7, 1, 257, 19684, 261, 6, 1, 65537, 7625597484988, 4294967313, 3126, 12, 1, 4294967297, 443426488243037769948249630619149892804, 340282366920938463463374607431768211713, 298023223876953126, 46688, 8
Offset: 1
Examples
Square array begins: 1, 1, 1, 1, ... 3, 5, 17, 257, ... 4, 28, 19684, 7625597484988, ... 7, 261, 4294967313, 340282366920938463463374607431768211713, ...
Links
- Seiichi Manyama, Antidiagonals n = 1..9, flattened
Programs
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Mathematica
T[n_, k_] := DivisorSum[n, #^(#^k) &]; Table[T[k, n - k], {n, 1, 7}, {k, 1, n}] // Flatten (* Amiram Eldar, May 11 2021 *)
Formula
L.g.f. of column k: -log(Product_{j>=1} (1 - x^j)^(j^(j^k-1))).