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

1,1

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,....

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A055574, A000203.

Sequence in context: A124936 A213063 A268281 * A068560 A039773 A289947

Adjacent sequences: A223134 A223135 A223136 * A223138 A223139 A223140

Keyword

nonn

Author

Jaroslav Krizek, May 01 2013

Extensions

Extended by T. D. Noe, May 02 2013

Status

approved