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A308694 Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{d|n} d^(k*(n/d - 1)), read by antidiagonals. 5
1, 1, 2, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 4, 2, 1, 2, 2, 6, 2, 4, 1, 2, 2, 10, 2, 9, 2, 1, 2, 2, 18, 2, 27, 2, 4, 1, 2, 2, 34, 2, 93, 2, 14, 3, 1, 2, 2, 66, 2, 339, 2, 82, 11, 4, 1, 2, 2, 130, 2, 1269, 2, 578, 83, 23, 2, 1, 2, 2, 258, 2, 4827, 2, 4354, 731, 283, 2, 6 (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+1))).

A(p,k) = 2 for prime p.

EXAMPLE

Square array begins:

   1, 1,  1,  1,   1,    1,    1, ...

   2, 2,  2,  2,   2,    2,    2, ...

   2, 2,  2,  2,   2,    2,    2, ...

   3, 4,  6, 10,  18,   34,   66, ...

   2, 2,  2,  2,   2,    2,    2, ...

   4, 9, 27, 93, 339, 1269, 4827, ...

   2, 2,  2,  2,   2,    2,    2, ...

CROSSREFS

Columns k=0..3 give A000005, A087909, A308692, A308693.

Cf. A308509, A308690.

Sequence in context: A053260 A267135 A140223 * A280521 A278043 A014643

Adjacent sequences:  A308691 A308692 A308693 * A308695 A308696 A308697

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jun 17 2019

STATUS

approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)