A221641 Square array read by antidiagonals T(n,k) in which column k lists 1 interleaved with j-1 zeros, if k = j^2 or k = j^2 + j, otherwise column k lists only zeros, with n>=1, j>=1, k>=1.

1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1

Comments

The number of ones in the n-th antidiagonal equals the number 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 ones 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 16 rows are
1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,...
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,...
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,...
1,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,...
1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
1,1,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,...
...
For n = 7 the 7th antidiagonal is 1,1,0,0,0,0,0. The number of ones is equal to d(7) = A000005(7) = 2.
For n = 16 the 16th antidiagonal is 1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,1. The number of ones is equal to d(16) = A000005(16) = 5.
The first few antidiagonals (compressed) are:
1     1
2     11
3     110
4     1101
5     11000
6     110101
7     1100000
8     11010100
9     110000001
10    1101010000
11    11000000000
12    110101001001
...

Crossrefs

Antidiagonal sums give A000005.

Cf. A000040, A002620, A049068, A051731, A063376, A210959, A221642.

Sequence in context: A071036 A071038 A131522 * A144473 A011750 A340375

Adjacent sequences: A221638 A221639 A221640 * A221642 A221643 A221644

Keyword

nonn,tabl

Author

Omar E. Pol, Jan 31 2013

Status

approved