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

Author

J. M. Bergot, Feb 12 2011

Keywords

• nonn
• more

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

Examples

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

Links

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

Programs

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

Extensions

a(15) from Giovanni Resta, Apr 04 2014