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

Author

Jaroslav Krizek, May 01 2013

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

Cf. A000203, A014574, A040040.

Programs

Mathematica

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