A159072 - OEIS

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

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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.