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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

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Last modified April 22 14:18 EDT 2021. Contains 343177 sequences. (Running on oeis4.)