A159073 - OEIS

%I #3 Mar 30 2012 19:00:15

%S 0,2,5,9,10,20,17,29,26,31,28,67,41,59,65,69,58,95,77,119,107,103,100,

%T 179,125,130,136,154,129,228,160,220,202,198,220,280,197,239,245,320,

%U 238,334,281,359,402,331,328,487,377,417,388,418,381,499,461,556,447,443,440

%N Sum of the 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.

%C Terms of the sum are counted in A159070.

%F a(n) = A158975(n) - 1.

%F If p = prime, element of A000040, a(p) = A158662(p) - 1 = A014284(A036234(p)) - 1.

%e a(8) = 29 is the sum of the following six 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} of n = 8. 2 + 3 + 4 + 5 + 7 + 8 = 29.

%Y Cf.: A158975, A000040, A014284, A036234.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Apr 04 2009

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