OFFSET
1,3
LINKS
Seiichi Manyama, Antidiagonals n = 1..140, flattened
FORMULA
G.f. of column k: Sum_{j>=1} sigma_k(j)*x^j/(1 - x^j).
A(n,k) = Sum_{d|n} d^k*tau(n/d).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
3, 4, 6, 10, 18, 34, ...
3, 5, 11, 29, 83, 245, ...
6, 11, 27, 83, 291, 1091, ...
3, 7, 27, 127, 627, 3127, ...
9, 20, 66, 290, 1494, 8330, ...
MATHEMATICA
Table[Function[k, Sum[DivisorSigma[k, d], {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
Table[Function[k, SeriesCoefficient[Sum[DivisorSigma[k, j] x^j/(1 - x^j), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
PROG
(PARI) T(n, k)={sumdiv(n, d, d^k*numdiv(n/d))}
for(n=1, 10, for(k=0, 8, print1(T(n, k), ", ")); print); \\ Andrew Howroyd, Nov 26 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Nov 26 2018
STATUS
approved