|
| |
|
|
A308690
|
|
Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{d|n} d^(k*n/d - k + 1), read by antidiagonals.
|
|
4
|
|
|
|
1, 1, 3, 1, 3, 4, 1, 3, 4, 7, 1, 3, 4, 9, 6, 1, 3, 4, 13, 6, 12, 1, 3, 4, 21, 6, 24, 8, 1, 3, 4, 37, 6, 66, 8, 15, 1, 3, 4, 69, 6, 216, 8, 41, 13, 1, 3, 4, 133, 6, 762, 8, 201, 37, 18, 1, 3, 4, 261, 6, 2784, 8, 1289, 253, 68, 12, 1, 3, 4, 517, 6, 10386, 8, 9225, 2197, 648, 12, 28
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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)^(1/j^k)).
A(p,k) = p+1 for prime p.
|
|
|
EXAMPLE
|
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
3, 3, 3, 3, 3, 3, 3, ...
4, 4, 4, 4, 4, 4, 4, ...
7, 9, 13, 21, 37, 69, 133, ...
6, 6, 6, 6, 6, 6, 6, ...
12, 24, 66, 216, 762, 2784, 10386, ...
8, 8, 8, 8, 8, 8, 8, ...
|
|
|
CROSSREFS
|
Columns k=0..3 give A000203, A055225, A308688, A308689.
Cf. A294579, A308509, A308694.
Sequence in context: A107638 A245093 A104765 * A329512 A064884 A093560
Adjacent sequences: A308687 A308688 A308689 * A308691 A308692 A308693
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Seiichi Manyama, Jun 17 2019
|
|
|
STATUS
|
approved
|
| |
|
|
