A221645 Square array read by antidiagonals: T(n,k^2) = A040000(n) (= 1,2,2,2,...) if n=0 (mod k), T(n,k) = 0 else, n>=0, k>=1.

1, 2, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Omar E. Pol, Feb 02 2013

Keywords

• nonn
• tabl

Comments

Other definition: Square array read by antidiagonal: T(n,k), n>=0, k>=1, in which column k lists the numbers A040000 (1, 2, 2, 2, 2...) interleaved with k^(1/2)-1 zeros, if k is a square otherwise column k lists only zeros.

The sum of elements of the n-th antidiagonal equals the number of divisors of n. In other words, the antidiagonal sums give A000005.

Examples

			First 16 elements of first 16 rows of the square array are
1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,...
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,...
2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,...
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,2,0,0,0,0,2,0,0,0,0,0,0,0,...
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,...
2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,...
2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,2,0,0,0,0,2,0,0,0,0,0,0,2,...
2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,...
2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,...
...
For n = 3 the sum of the third antidiagonal is 2+0+0 = d(3) = A000005(3) = 2.
For n = 16 the sum of the 16th antidiagonal is 2+0+0+2+0+0+0+0+0+0+0+0+0+0+0+1 = d(16) = A000005(16) = 5.
		

Crossrefs

Cf. A000005, A212119.

Programs

PARI

A221645(n,m)={my(t); issquare(m,&t)||return; n||return(1); n%t & return;2} \\ M. F. Hasler, Feb 02 2013

Formula

sum_{k=1...n} a(n-k,k) = A000005(n) for all n>0. - M. F. Hasler, Feb 02 2013