A186103 Numbers k such that k | sigma(k-1) + sigma(k+1).

13, 77, 489, 557, 1101, 1431, 2409, 8897, 538209, 2263024, 8910721, 13685781, 17428321, 962402769, 128508838576

Offset

1,1

Comments

The calculations were produced by V. Astanoff and Richard Tobin. Tobin has found that there are no other solutions up to 2*10^9.

a(16) > 10^13. - Giovanni Resta, Apr 04 2014

Links

Table of n, a(n) for n=1..15.

J. M. Bergot, et al., How rare is 13?, sci.math discussion

Example

Take consecutive numbers 8896, 8897, 8898 to find that sigma(8896)=17780 and sigma(8898)=17808, with sum 35588=4*8897.

Prog

(PARI) sa=sigma(1); sb=sigma(2); for(n=2, 1e10, sc=sigma(n+1); if((sa+sc)%n==0, print1(n", ")); sa=sb; sb=sc) \\ Charles R Greathouse IV, Feb 13 2011

Crossrefs

Sequence in context: A044581 A126423 A072474 * A194713 A047638 A010929

Adjacent sequences: A186100 A186101 A186102 * A186104 A186105 A186106

Keyword

nonn,more

Author

J. M. Bergot, Feb 12 2011

Extensions

a(15) from Giovanni Resta, Apr 04 2014

Status

approved