A127571 Triangle T(n,k) = phi(n/k)*sigma(k) if k divides n, else 0.

1, 1, 3, 2, 0, 4, 2, 3, 0, 7, 4, 0, 0, 0, 6, 2, 6, 4, 0, 0, 12, 6, 0, 0, 0, 0, 0, 8, 4, 6, 0, 7, 0, 0, 0, 15, 6, 0, 8, 0, 0, 0, 0, 0, 13, 4, 12, 0, 0, 6, 0, 0, 0, 0, 18

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Formula

T(n,k) = sum_{j=k..n} A054523(n,j)* A130208(j,k), product of the two infinite lower triangular matrices.

T(n,1) = A000010(n).

T(n,n) = A000203(n).

Example

First few rows of the triangle are:
1;
1, 3;
2, 0, 4;
2, 3, 0, 7;
4, 0, 0, 0, 6;
2, 6, 4, 0, 0, 12;
...

Crossrefs

Cf. A000203, A000010, A038040 (row sums), A054523.

Sequence in context: A341413 A290794 A328178 * A194662 A143612 A353160

Adjacent sequences: A127568 A127569 A127570 * A127572 A127573 A127574

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 19 2007

Status

approved