A096180 Triangle read by rows: fraction of integers having k of the first n positive integers as divisors is T(n,k)/A003418(n).

1, 1, 1, 2, 3, 1, 4, 4, 3, 1, 16, 20, 16, 7, 1, 16, 20, 12, 6, 5, 1, 96, 136, 92, 48, 36, 11, 1, 192, 272, 136, 124, 66, 38, 11, 1, 576, 720, 464, 360, 206, 122, 58, 13, 1, 576, 720, 392, 384, 188, 154, 70, 26, 9, 1, 5760, 7776, 4640, 4232, 2264, 1728, 854, 330, 116, 19

Offset: 1

Author

Matthew Vandermast, Jun 19 2004

Keywords

• nonn
• tabl

Comments

Sum of entries in n-th row is A003418(n), the least common multiple of integers 1 to n.

Examples

			Triangle begins:
1
1 1
2 3 1
4 4 3 1
16 20 16 7 1
16 20 12 6 5 1
		

Crossrefs

Cf. A003418, A217863 (first column).

Programs

PARI

lcmn(n) = lcm(vector(n, k, k));
rowd(n) = {v = vector(n); for (k=1, lcmn(n), d = divisors(k); v[sum(j=1, #d, d[j]<=n)]++;); v;} \\ Michel Marcus, Apr 29 2017