login
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
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
1,2
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).
EXAMPLE
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;
...
CROSSREFS
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.
Sequence in context: A154860 A284282 A132774 * A300816 A007945 A011150
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Nov 07 2017
STATUS
approved