OFFSET
1,10
COMMENTS
A(n,k) is the sum of k-th powers of proper divisors of n.
LINKS
Eric Weisstein's World of Mathematics, Proper divisors
FORMULA
G.f. of column k: Sum_{j>=1} j^k*x^(2*j)/(1 - x^j).
Dirichlet g.f. of column k: zeta(s-k)*(zeta(s) - 1).
A(n,k) = 1 if n is prime.
EXAMPLE
Square array begins:
0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
2, 3, 5, 9, 17, 33, ...
1, 1, 1, 1, 1, 1, ...
3, 6, 14, 36, 98, 276, ...
MATHEMATICA
Table[Function[k, DivisorSigma[k, n] - n^k][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
Table[Function[k, SeriesCoefficient[Sum[j^k x^(2 j)/(1 - x^j), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Nov 01 2018
STATUS
approved