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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 12:38 EST 2023. Contains 359945 sequences. (Running on oeis4.)