|
|
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).
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|