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A308676
Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(d^k * n/d).
4
1, 1, 3, 1, 5, 4, 1, 17, 28, 9, 1, 257, 19684, 273, 6, 1, 65537, 7625597484988, 4294967553, 3126, 24, 1, 4294967297, 443426488243037769948249630619149892804, 340282366920938463463374607431768276993, 298023223876953126, 47450, 8
OFFSET
1,3
LINKS
FORMULA
L.g.f. of column k: -log(Product_{j>=1} (1 - j^(j^k) * x^j)^(1/j)).
EXAMPLE
Square array begins:
1, 1, 1, 1, ...
3, 5, 17, 257, ...
4, 28, 19684, 7625597484988, ...
9, 273, 4294967553, 340282366920938463463374607431768276993, ...
MATHEMATICA
T[n_, k_] := DivisorSum[n, #^(n * #^(k-1)) &]; Table[T[k, n - k], {n, 1, 7}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *)
CROSSREFS
Columns k=0..3 give A055225, A023887, A308670, A308675.
Cf. A308674.
Sequence in context: A294579 A308502 A308674 * A131809 A016574 A210560
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jun 16 2019
STATUS
approved