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).

1, 1, 3, 1, 5, 4, 1, 17, 28, 9, 1, 257, 19684, 273, 6, 1, 65537, 7625597484988, 4294967553, 3126, 24, 1, 4294967297, 443426488243037769948249630619149892804, 340282366920938463463374607431768276993, 298023223876953126, 47450, 8

Offset

1,3

Links

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

Formula

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

Example

Square array begins:
   1,    1,          1,                                       1, ...
   3,    5,         17,                                     257, ...
   4,   28,      19684,                           7625597484988, ...
   9,  273, 4294967553, 340282366920938463463374607431768276993, ...

Mathematica

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 *)

Crossrefs

Columns k=0..3 give A055225, A023887, A308670, A308675.

Cf. A308674.

Sequence in context: A294579 A308502 A308674 * A131809 A016574 A210560

Adjacent sequences: A308673 A308674 A308675 * A308677 A308678 A308679

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 16 2019

Status

approved