A141846 Triangle read by rows: A051731 * A051953^(n-k) * 0^(n-k), 1 <= k <= n.

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

Offset

1,10

Comments

Row sums = A001065: (0, 1, 1, 3, 1, 6, 1, 7, 4, 8,...).

n-th row = (p-1) zeros followed by 1, iff n is prime.

For T(n,k), k divides n if k not = 0.

Links

Table of n, a(n) for n=1..105.

Formula

Triangle read by rows, A051731 * A051953^(n-k); where A051953^(n-k) = an infinite lower triangular matrix with A051953 (0, 1, 1, 2, 1, 4, 1, 4, 3, 6, 1, 8,...) in the main diagonal and the rest zeros. A051731 = inverse Mobius transform.

Example

First few rows of the triangle =
0;
0, 1;
0, 0, 1;
0, 1, 0, 2;
0, 0, 0, 0, 1;
0, 1, 1, 0, 0, 4;
0, 0, 0, 0, 0, 0, 1;
0, 1, 0, 2, 0, 0, 0, 4;
0, 0, 1, 0, 0, 0, 0, 0, 3;
0, 1, 0, 0, 1, 0, 0, 0, 0, 6;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
0, 1, 1, 2, 0, 4, 0, 0, 0, 0, 0, 8;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8;
...

Crossrefs

Cf. A051953, A001065.

Sequence in context: A262900 A242830 A101668 * A188171 A363807 A330733

Adjacent sequences: A141843 A141844 A141845 * A141847 A141848 A141849

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 11 2008

Status

approved