A223136 Numbers n such that sigma(n+1) - sigma(n) = k*n for some integer k, where sigma(n) = A000203 (sum of divisors of n).

1, 3, 7, 14, 31, 127, 206, 532, 954, 957, 1334, 1364, 1634, 2685, 2974, 4364, 8191, 14841, 18873, 19358, 20145, 24957, 33998, 36566, 42818, 56564, 64665, 74918, 79826, 79833, 84134, 92685, 104944, 109214, 111506, 116937, 122073, 131071, 138237, 147454, 161001

Offset: 1

Author

Jaroslav Krizek, May 01 2013

Keywords

• nonn

Comments

Supersequence of A000668 for k=1 (Mersenne primes), A067803 for k=-1 (numbers n such that sigma(n) - sigma(n+1) = n) and A002961 for k=0 (numbers n such that n and n+1 have same sum of divisors). For number 1 is k=2.

Corresponding values of integers k: 2, 1, 1, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,....

Examples

			Number 532 is in sequence because sigma(533) - sigma(532) = 588 - 1120 = -532 = (-1) * 532; k = -1.
		

Links

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

Crossrefs

Cf. A000668, A067803, A002961, A000203.

Programs

Mathematica

Select[Range[10000], IntegerQ[(DivisorSigma[1, # + 1] - DivisorSigma[1, #])/#] &] (* T. D. Noe, May 02 2013 *)

Extensions

Extended by T. D. Noe, May 02 2013