A159073 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.

0, 2, 5, 9, 10, 20, 17, 29, 26, 31, 28, 67, 41, 59, 65, 69, 58, 95, 77, 119, 107, 103, 100, 179, 125, 130, 136, 154, 129, 228, 160, 220, 202, 198, 220, 280, 197, 239, 245, 320, 238, 334, 281, 359, 402, 331, 328, 487, 377, 417, 388, 418, 381, 499, 461, 556, 447, 443, 440

Offset

1,2

Comments

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

Terms of the sum are counted in A159070.

Links

Table of n, a(n) for n=1..59.

Formula

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

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

Example

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.

Crossrefs

Cf.: A158975, A000040, A014284, A036234.

Sequence in context: A249353 A224866 A348167 * A088343 A110781 A170838

Adjacent sequences: A159070 A159071 A159072 * A159074 A159075 A159076

Keyword

nonn

Author

Jaroslav Krizek, Apr 04 2009

Extensions

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

Status

approved