A015863 Numbers k such that sigma(k) = sigma(k+4).

51, 66, 115, 220, 319, 1003, 2585, 4024, 4183, 4195, 5720, 5826, 5959, 8004, 8374, 11659, 12367, 12561, 13581, 14338, 15365, 16116, 17840, 18718, 20541, 25130, 29393, 30170, 32665, 36516, 39913, 40660, 42423, 42922, 47841, 49762

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 51, p. 19, Ellipses, Paris 2008.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 130 terms from Paolo P. Lava)
• 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, A015865, A015866, A015867, A015876, A015877, A015880, A015881, A015882, A015883, A181647.

Programs

Mathematica

Select[Range[60000], DivisorSigma[1, #]==DivisorSigma[1, # + 4] &] (* Vincenzo Librandi, Mar 10 2014 *)
SequencePosition[DivisorSigma[1,Range[50000]],{x_,,,_,x_}][[;;,1]] (* Harvey P. Dale, Feb 13 2025 *)

PARI

is(n)=sigma(n)==sigma(n+4) \\ Charles R Greathouse IV, Mar 09 2014