A221642 Square array read by antidiagonals: T(n,k) in which if k = j^2 then column k lists j interleaved with j-1 zeros. Otherwise if k = j^2 + j then column k lists the positive integers, starting with j+1, interleaved with j-1 zeros. Otherwise column k lists only zeros. n>=1, j>=1, k>=1.

1, 1, 2, 1, 3, 0, 1, 4, 0, 2, 1, 5, 0, 0, 0, 1, 6, 0, 2, 0, 3, 1, 7, 0, 0, 0, 0, 0, 1, 8, 0, 2, 0, 4, 0, 0, 1, 9, 0, 0, 0, 0, 0, 0, 3, 1, 10, 0, 2, 0, 5, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 0, 2, 0, 6, 0, 0, 3, 0, 0, 4, 1, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,3

Comments

The number of positive terms in the n-th antidiagonal equals the number of divisors of n.

The sum of the elements of n-th antidiagonal equals the sum of divisors of n.

All terms of column k are zeros iff k is not a quarter-square A002620.

If only the first two elements are positive integers in the n-th antidiagonal then n is prime.

Links

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

Example

First 24 elements of first 8 rows of the square array are
1,2,0,2,0,3,0,0,3,0,0,4,0,0,0,4,0,0,0,5,0,0,0,0,...
1,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,4,0,2,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,5,0,0,0,0,0,0,3,0,0,5,0,0,0,0,0,0,0,0,0,0,0,0,...
1,6,0,2,0,5,0,0,0,0,0,0,0,0,0,4,0,0,0,6,0,0,0,0,...
1,7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,8,0,2,0,6,0,0,3,0,0,6,0,0,0,0,0,0,0,0,0,0,0,0,...
1,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...

Crossrefs

Antidiagonal sums give A000203.

Cf. A000005, A002620, A210959, A221641.

Sequence in context: A194893 A141673 A127094 * A158906 A309229 A143239

Adjacent sequences: A221639 A221640 A221641 * A221643 A221644 A221645

Keyword

nonn,tabl

Author

Omar E. Pol, Jan 31 2013

Status

approved