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

1,5

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.

Links

Table of n, a(n) for n=1..77.

Formula

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

Example

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.

Sequence in context: A029139 A100927 A001687 * A116928 A239948 A034391

Adjacent sequences: A159069 A159070 A159071 * A159073 A159074 A159075

Keyword

nonn

Author

Jaroslav Krizek, Apr 04 2009

Extensions

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

Status

approved