A308502 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{d|n} d^(n/d + k).

1, 1, 3, 1, 5, 4, 1, 9, 10, 9, 1, 17, 28, 25, 6, 1, 33, 82, 81, 26, 24, 1, 65, 244, 289, 126, 80, 8, 1, 129, 730, 1089, 626, 330, 50, 41, 1, 257, 2188, 4225, 3126, 1604, 344, 161, 37, 1, 513, 6562, 16641, 15626, 8634, 2402, 833, 163, 68, 1, 1025, 19684, 66049, 78126, 49100, 16808, 5249, 973, 290, 12

Offset

1,3

Links

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

Formula

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

Example

Square array begins:
    1,  1,   1,    1,    1,     1, ...
    3,  5,   9,   17,   33,    65, ...
    4, 10,  28,   82,  244,   730, ...
    9, 25,  81,  289, 1089,  4225, ...
    6, 26, 126,  626, 3126, 15626, ...
   24, 80, 330, 1604, 8634, 49100, ...

Mathematica

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

Crossrefs

Columns k=0..2 give A055225, A078308, A296601.

Cf. A279394, A308504.

Sequence in context: A124883 A319278 A294579 * A308674 A308676 A131809

Adjacent sequences: A308499 A308500 A308501 * A308503 A308504 A308505

Keyword

nonn,tabl

Author

Seiichi Manyama, Jun 02 2019

Status

approved