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A212119
Triangle read by rows T(n,k), n>=1, k>=1, where T(n,k) is the number of divisors d of n with min(d, n/d) = k.
13
1, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0
OFFSET
1,2
COMMENTS
Column k lists the numbers A040000: 1, 2, 2, 2, 2... interleaved with k-1 zeros, starting in row k^2.
The sum of row n gives A000005(n), the number of divisors of n.
T(n,k) is also the number of divisors of n on the edges of k-th triangle in the diagram of divisors (see link section). See also A212120.
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. - Omar E. Pol, Dec 03 2013
EXAMPLE
Row 10 gives 2, 2, 0 therefore the sums of row 10 is 2+2+0 = 4, the same as A000005(10), the number of divisors of 10.
Written as an irregular triangle the sequence begins:
1;
2;
2;
2, 1;
2, 0;
2, 2;
2, 0;
2, 2;
2, 0, 1;
2, 2, 0;
2, 0, 0;
2, 2, 2;
2, 0, 0;
2, 2, 0;
2, 0, 2;
2, 2, 0, 1;
2, 0, 0, 0;
2, 2, 2, 0;
2, 0, 0, 0;
2, 2, 0, 2;
2, 0, 2, 0;
2, 2, 0, 0;
2, 0, 0, 0;
2, 2, 2, 2;
2, 0, 0, 0, 1;
CROSSREFS
Row sums give A000005. Column 1 is A040000. Column 2 gives the absolute values of A176742.
Sequence in context: A129320 A359556 A320844 * A096831 A191516 A168141
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Jul 02 2012
EXTENSIONS
Definition changed by Franklin T. Adams-Watters, Jul 12 2012
STATUS
approved