A015866 Numbers k such that sigma(k) = sigma(k+6).

20, 155, 182, 184, 203, 264, 621, 650, 702, 852, 893, 944, 1343, 1357, 2024, 2544, 2990, 4130, 4183, 4450, 5428, 5835, 6149, 6313, 6572, 8177, 8695, 11208, 11333, 11991, 12444, 12561, 12859, 13595, 14857, 16815, 18203, 18330, 18430, 19089

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

Up to 10^13, sigma(k-6) = sigma(k) = sigma(k+6) only for k = 33227, 604453 and 4223105512993. - Giovanni Resta, Mar 03 2014

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 20, pp 7, Ellipses, Paris 2008.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Donovan Johnson)
• A. Weingartner, On the Solutions of sigma(n) = sigma(n+k), Journal of Integer Sequences, Vol. 14 (2011), #11.5.5.

Crossrefs

Cf. A002961, A007373, A015861, A015863, A015865, A015867, A015876, A015877, A015880, A015881, A015882, A015883, A181647.

Programs

Mathematica

Select[Range[20000], DivisorSigma[1, #]==DivisorSigma[1, # + 6] &] (* Vincenzo Librandi, Mar 10 2014 *)

PARI

is(n)=sigma(n)==sigma(n+6) \\ Charles R Greathouse IV, Mar 09 2014