A294721 Irregular triangle read by rows: T(n,k) = n if k is the largest divisor of n <= sqrt(n), otherwise T(n,k) = 0. The first element of column k is in row k^2, n>=1, k>=1.

1, 2, 3, 0, 4, 5, 0, 0, 6, 7, 0, 0, 8, 0, 0, 9, 0, 10, 0, 11, 0, 0, 0, 0, 12, 13, 0, 0, 0, 14, 0, 0, 0, 15, 0, 0, 0, 16, 17, 0, 0, 0, 0, 0, 18, 0, 19, 0, 0, 0, 0, 0, 0, 20, 0, 0, 21, 0, 0, 22, 0, 0, 23, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 25, 0, 26, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 28, 0, 29, 0, 0, 0, 0, 0, 0, 0, 0, 30

Offset: 1

Author

Omar E. Pol, Nov 07 2017

Keywords

• nonn
• tabf

Examples

			Triangle begins:
1;
2;
3;
0,   4;
5,   0;
0,   6;
7,   0;
0,   8;
0,   0,   9;
0,  10,   0;
11,  0,   0;
0,   0,  12;
13,  0,   0;
0,  14,   0;
0,   0,  15;
0,   0,   0,  16;
17,  0,   0,   0;
0,   0,  18,   0;
19,  0,   0,   0;
0,   0,   0,  20;
0,   0,  21,   0;
0,  22,   0,   0;
23,  0,   0,   0;
0,   0,   0,  24;
0,   0,   0,   0,  25;
...
		

Links

• Omar E. Pol, Illustration of initial terms

Crossrefs

Cf. A033676, A163280, A294821.

Row n has length A000196(n).

Row sums give A000027.

Positive terms also give A000027.

Positive terms of column k, for k = 1..12, give respectively: A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.

Formula

T(n, A033676(n)) = n.

T(n,k) = 0, if k is not equal to A033676(n), n >= 1, and 1 <= k <= A000196(n).

T(n,k) = n*A294821(n,k).