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A356045

Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} sigma_k(j) * floor(n/j).

1, 1, 4, 1, 5, 7, 1, 7, 10, 13, 1, 11, 18, 21, 16, 1, 19, 40, 45, 28, 25, 1, 35, 102, 123, 72, 48, 28, 1, 67, 280, 393, 250, 138, 57, 38, 1, 131, 798, 1371, 1020, 540, 189, 83, 44, 1, 259, 2320, 5025, 4498, 2514, 885, 301, 101, 53, 1, 515, 6822, 18963, 20652, 12828, 4917, 1553, 403, 129, 56

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OFFSET

1,3

LINKS

Seiichi Manyama, Antidiagonals n = 1..140, flattened

FORMULA

G.f. of column k: (1/(1-x)) * Sum_{j>=1} sigma_k(j) * x^j/(1 - x^j).

T(n,k) = Sum_{j=1..n} Sum_{d|j} d^k * tau(j/d).

T(n,k) = Sum_{j=1..n} Sum_{d|j} sigma_k(d).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, ...