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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.
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%I #7 Mar 31 2020 10:52:04

%S 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,

%T 17,11,15,13,13,13,19,12,14,14,19,13,19,14,18,19,16,15,24,16,19,17,19,

%U 16,22,18,23,18,18,17,28,18,20,23,23,20,24,19,23,21,26,20,31,21,23,25,25

%N 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.

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

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

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

%e 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.

%Y Cf. A158973, A000040, A036234, A000720.

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Apr 04 2009

%E Edited and extended by _R. J. Mathar_, Apr 06 2009