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

1,2

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,....

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A000668, A067803, A002961, A000203.

Sequence in context: A011947 A129629 A354463 * A354603 A089526 A261051

Adjacent sequences: A223133 A223134 A223135 * A223137 A223138 A223139

Keyword

nonn

Author

Jaroslav Krizek, May 01 2013

Extensions

Extended by T. D. Noe, May 02 2013

Status

approved