A138553 Table read by rows: T(n,k) is the number of divisors of k that are <= n.

1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 2, 3, 1, 3, 2, 3, 1, 4, 1, 2, 3, 3, 1, 3, 1, 4, 2, 2, 1, 4, 2, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 4, 1, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 5, 1, 2, 2, 3, 2, 4, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 1, 4, 1, 4, 2, 2, 1, 5

Offset: 1

Author

Franklin T. Adams-Watters, Mar 24 2008

Keywords

• easy
• nonn
• tabf

Comments

Suggested by a question from Eric Desbiaux.

The row lengths are the lengths before the pattern for n repeats.

Antidiagonal sums A070824. [From Eric Desbiaux, Dec 10 2009]

Examples

			The first few rows start:
1, [A000012]
1, 2, [A000034]
1, 2, 2, 2, 1, 3, [A083039]
1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, [A083040]
		

Crossrefs

Row lengths A003418, row sums A025529, frequencies in rows A096180.

Cf. A243987

Programs

PARI

lista(nrows) = {for (n=1, nrows, for (k=1, lcm(vector(n, i, i)), print1(sumdiv(k, d, d <=n), ", ");); print(););} \\ Michel Marcus, Jun 19 2014

Formula

T(n,k) = sum_{i|k, i<=n} 1.

Extensions

Definition corrected by Franklin T. Adams-Watters, Jun 19 2014