A127476 Triangle T(n,k) = sum_{j=k..n, gcd(n,j)=1, k|j} phi(k).

1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, 2, 0, 0, 0, 4, 0, 6, 3, 4, 2, 4, 2, 0, 4, 0, 2, 0, 4, 0, 6, 0, 6, 3, 0, 4, 4, 0, 6, 4, 0, 4, 0, 4, 0, 0, 0, 6, 0, 6, 0, 10, 5, 6, 4, 8, 2, 6, 4, 6, 4, 0, 4, 0, 0, 0, 4, 0, 6, 0, 0, 0, 10, 0

Offset

1,4

Links

Table of n, a(n) for n=1..78.

Formula

T(n,k) = sum_{j=k..n} A054521(n,j) * A054522(j,k), product of the two infinite lower triangular matrices.

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

Example

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

Crossrefs

Cf. A054521, A054522, A023896 (row sums), A000010.

Sequence in context: A244553 A231167 A194313 * A140397 A120614 A287516

Adjacent sequences: A127473 A127474 A127475 * A127477 A127478 A127479

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 15 2007

Status

approved