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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
OFFSET
1,3
LINKS
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, ...
MATHEMATICA
T[n_, k_] := DivisorSum[n, #^(k*(n/# - 1)) &]; Table[T[k, n - k], {n, 1, 12}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *)
CROSSREFS
Columns k=0..3 give A000005, A087909, A308692, A308693.
Sequence in context: A053260 A267135 A140223 * A280521 A278043 A014643
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jun 17 2019
STATUS
approved