A223137 Numbers n such that sigma(n+1) - sigma(n-1) = k*n for some integer k, where sigma(n) = A000203 (sum of divisors of n).

5, 34, 55, 285, 367, 835, 849, 919, 1241, 1505, 2911, 2914, 3305, 4149, 4188, 6111, 6903, 7170, 7913, 9360, 10251, 10541, 12566, 15086, 17273, 17815, 19005, 19689, 21411, 21462, 24882, 25020, 26610, 28125, 30593, 30789, 31485, 38211, 38983, 39787, 40311, 45355

Offset: 1

Author

Jaroslav Krizek, May 01 2013

Keywords

• nonn

Comments

Supersequence of A055574 for k=0 (n satisfying sigma(n+1) = sigma(n-1)). For number 5 is k=1. Are there other such number for k=1 or k=-1?

Corresponding values of integers k: 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,....

Examples

			Number 5 is in sequence because sigma(6) - sigma(4) = 12 - 7 = 5 = 1 * 5; k=1.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055574, A000203.

Programs

Mathematica

Select[Range[100000], IntegerQ[(DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1])/#] &] (* T. D. Noe, May 02 2013 *)

Extensions

Extended by T. D. Noe, May 02 2013