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

1,3

Links

Seiichi Manyama, Antidiagonals n = 1..9, flattened

Formula

L.g.f. of column k: -log(Product_{j>=1} (1 - x^j)^(j^(j^k-1))).

Example

Square array begins:
   1,   1,          1,                                       1, ...
   3,   5,         17,                                     257, ...
   4,  28,      19684,                           7625597484988, ...
   7, 261, 4294967313, 340282366920938463463374607431768211713, ...

Mathematica

T[n_, k_] := DivisorSum[n, #^(#^k) &]; Table[T[k, n - k], {n, 1, 7}, {k, 1, n}] // Flatten (* Amiram Eldar, May 11 2021 *)

Crossrefs

Columns k=0..3 give A000203, A062796, A308671, A308672.

Cf. A308676.

Sequence in context: A319278 A294579 A308502 * A308676 A131809 A016574

Adjacent sequences: A308671 A308672 A308673 * A308675 A308676 A308677

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 16 2019

Status

approved