A223138 Numbers n such that sigma(n+1) - sigma(n-1) = n / k for some integer, where sigma(n) = A000203 (sum of divisors of n).

4, 5, 6, 9, 10, 12, 18, 30, 32, 42, 54, 56, 60, 72, 101, 102, 108, 129, 138, 144, 150, 172, 176, 180, 192, 198, 204, 216, 220, 228, 240, 252, 270, 282, 312, 348, 384, 420, 432, 462, 522, 544, 570, 600, 618, 642, 648, 660, 792, 810, 822, 828, 858, 882, 900, 1020

Offset

1,1

Comments

Supersequence of A014574 for k = n/2 (average of twin prime pairs).

Corresponding values of integers k: 2, 1, 3, 3, -10, 6, 9, 15, 2, 21, 3, 7, 30, 36, -101, 51, 54, -43, 69, 12, 75, -2, -22, 90, 96, 99, 17, -27, -5, 114, 120, 7, 135, 141, 156, 174, 2, 210, 216, 231, 261, -8, 285, 300, 309, 321, 9, 330, -18, 405, 411, 414, 429, 441, 75, 510, ... (supersequence of A040040).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

Select[Range[1000], DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1] != 0 && IntegerQ[#/(DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1])] &] (* T. D. Noe, May 02 2013 *)

Crossrefs

Cf. A000203, A014574, A040040.

Sequence in context: A062726 A159629 A328173 * A287676 A082812 A255634

Adjacent sequences: A223135 A223136 A223137 * A223139 A223140 A223141

Keyword

nonn

Author

Jaroslav Krizek, May 01 2013

Status

approved