A159072 Count of numbers k in the range 1<=k<= n such that set of proper divisors of k is not a subset of the set of the proper divisors of n.

1, 1, 1, 1, 2, 1, 3, 2, 4, 4, 6, 2, 7, 6, 7, 7, 10, 7, 11, 8, 11, 12, 14, 8, 15, 15, 16, 15, 19, 13, 20, 17, 20, 21, 22, 17, 25, 24, 25, 21, 28, 23, 29, 26, 26, 30, 32, 24, 33, 31, 34, 33, 37, 32, 37, 33, 39, 40, 42, 32, 43, 42, 40, 41, 45, 42, 48, 45, 48, 44, 51, 41, 52, 51, 50, 51, 54

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.

We use the (nonstandard) terminology that the empty set (the proper divisors of 1) is not a subset of another set.

Examples

			a(8) = 2 counts k=6 with divisors set {1, 2, 3} (not subset of the divisors {1, 2, 4} of n = 8), and k=1 without proper divisors.
		

Crossrefs

Cf.: A158974, A000040, A036234, A000720.

Formula

a(n)+A159070(n) = n. - R. J. Mathar, Apr 06 2009

Extensions

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