

A308690


Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{dn} 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
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OFFSET

1,3


LINKS



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, ...


MATHEMATICA

T[n_, k_] := DivisorSum[n, #^(k*n/#  k + 1) &]; Table[T[k, n  k], {n, 1, 12}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *)


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



