A228814 Triangle read by rows T(n,k), n>=1, k>=1, in which column k starts in row A002620(k+1). If k is odd the column k lists j's interleaved with (k-1)/2 zeros, where j = (k+1)/2. Otherwise, if k is even the column k lists the positive integers but starting from k/2+1, interleaved with (k-2)/2 zeros.

1, 1, 2, 1, 3, 1, 4, 2, 1, 5, 0, 1, 6, 2, 3, 1, 7, 0, 0, 1, 8, 2, 4, 1, 9, 0, 0, 3, 1, 10, 2, 5, 0, 1, 11, 0, 0, 0, 1, 12, 2, 6, 3, 4, 1, 13, 0, 0, 0, 0, 1, 14, 2, 7, 0, 0, 1, 15, 0, 0, 3, 5, 1, 16, 2, 8, 0, 0, 4, 1, 17, 0, 0, 0, 0, 0, 1, 18, 2, 9, 3, 6, 0

Offset: 1

Author

Omar E. Pol, Oct 03 2013

Keywords

• nonn
• tabf

Comments

The number of positive terms of row n is A000005(n).

The positive terms of row n are the divisors of n.

The number of zeros in row n equals A078152(n).

Row n has length A055086(n).

The sum of row n is A000203(n).

Positive terms give A210959.

It appears that there are only eight rows that do not contain zeros. The indices of these rows are 1, 2, 3, 4, 6, 8, 12, 24, the divisors of 24, see A018253.

For another version see A228812.

Examples

			For n = 60 the 60th row of triangle is [1, 60, 2, 30, 3, 20, 4, 15, 5, 12, 6, 10, 0, 0]. The row length is A055086(60) = 14. The number of zeros is A078152(60) = 2. The number of positive terms is A000005(60) = 12. The row sum is A000203(60) = 168.
Triangle begins:
1;
1,  2;
1,  3;
1,  4,  2;
1,  5,  0;
1,  6,  2,  3;
1,  7,  0,  0;
1,  8,  2,  4;
1,  9,  0,  0,  3;
1, 10,  2,  5,  0;
1, 11,  0,  0,  0;
1, 12,  2,  6,  3,  4;
1, 13,  0,  0,  0,  0;
1, 14,  2,  7,  0,  0;
1, 15,  0,  0,  3,  5;
1, 16,  2,  8,  0,  0,  4;
1, 17,  0,  0,  0,  0,  0;
1, 18,  2,  9,  3,  6,  0;
1, 19,  0,  0,  0,  0,  0;
1, 20,  2, 10,  0,  0,  4,  5;
1, 21,  0,  0,  3,  7,  0,  0;
1, 22,  2, 11,  0,  0,  0,  0;
1, 23,  0,  0,  0,  0,  0,  0;
1, 24,  2, 12,  3,  8,  4,  6;
...
		

Crossrefs

Column 1 is A000012.

Cf. A000005, A000203, A002620, A004526, A018253, A027750, A055086, A078152, A147861, A161904, A196020, A210959, A212119, A212120, A221645, A228812, A228813, A229940, A229942, A228944, A229950, A228951.