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

1,2

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.

Links

Table of n, a(n) for n=1..91.

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A000005, A212119.

Sequence in context: A227618 A366533 A340683 * A216176 A359007 A128765

Adjacent sequences: A221642 A221643 A221644 * A221646 A221647 A221648

Keyword

nonn,tabl

Author

Omar E. Pol, Feb 02 2013

Status

approved