A294579 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(1 + k*n/d).

1, 1, 3, 1, 5, 4, 1, 9, 10, 7, 1, 17, 28, 25, 6, 1, 33, 82, 97, 26, 12, 1, 65, 244, 385, 126, 80, 8, 1, 129, 730, 1537, 626, 588, 50, 15, 1, 257, 2188, 6145, 3126, 4508, 344, 161, 13, 1, 513, 6562, 24577, 15626, 35652, 2402, 2049, 163, 18

Offset

1,3

Links

Seiichi Manyama, Antidiagonals n = 1..140, flattened

Formula

L.g.f. of column k: -log(Product_{j>=1} (1 - j^k * x^j)). - Seiichi Manyama, Jun 02 2019

G.f. of column k: Sum_{j>0} j^(k+1) * x^j / (1 - j^k * x^j). - Seiichi Manyama, Jan 14 2023

Example

Square array begins:
  1,  1,   1,   1,    1, ...
  3,  5,   9,  17,   33, ...
  4, 10,  28,  82,  244, ...
  7, 25,  97, 385, 1537, ...
  6, 26, 126, 626, 3126, ...

Crossrefs

Columns k=0..2 give A000203, A078308, A294567.

Rows k=0..1 give A000012, A000051(n+1).

Cf. A292166, A292193.

Sequence in context: A110813 A124883 A319278 * A308502 A308674 A308676

Adjacent sequences: A294576 A294577 A294578 * A294580 A294581 A294582

Keyword

nonn,tabl

Author

Seiichi Manyama, Nov 02 2017

Status

approved