A159070 Count of numbers k in the range 1 < k <= n such that set of proper divisors of k is a subset of the set of proper divisors of n.

0, 1, 2, 3, 3, 5, 4, 6, 5, 6, 5, 10, 6, 8, 8, 9, 7, 11, 8, 12, 10, 10, 9, 16, 10, 11, 11, 13, 10, 17, 11, 15, 13, 13, 13, 19, 12, 14, 14, 19, 13, 19, 14, 18, 19, 16, 15, 24, 16, 19, 17, 19, 16, 22, 18, 23, 18, 18, 17, 28, 18, 20, 23, 23, 20, 24, 19, 23, 21, 26, 20, 31, 21, 23, 25, 25

Offset: 1

Author

Jaroslav Krizek, Apr 04 2009

Keywords

• nonn

Comments

Here proper divisors include 1 but not the argument (k or n, respectively) in the divisor set, as defined in A032741.

Examples

			a(8) = 6 admits the following 6 k: 2 {1}, 3 {1}, 4 {1, 2}, 5 {1}, 7 {1}, 8 {1, 2, 4} with subsets of the proper divisors {1, 2, 4} for n = 8.
		

Crossrefs

Cf. A158973, A000040, A036234, A000720.

Formula

a(n) = A158973(n) - 1.

If p = prime, element of A000040, a(p) = A158973(p) - 1 = A036234(p) - 1 = A000720(p).

Extensions

Edited and extended by R. J. Mathar, Apr 06 2009