A159073 Sum of the k in the range 1

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

Author

Jaroslav Krizek, Apr 04 2009

Keywords

• nonn

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.

Examples

			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.

Formula

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

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

Extensions

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