A067816 Numbers k such that sigma(k+1) - sigma(k) = k + 1.

1, 5, 8585, 16119, 29886159

Offset: 1

Author

Benoit Cloitre, Feb 08 2002

Keywords

• nonn
• more

Comments

Mersenne primes are solutions of sigma(x+1) - sigma(x) = x.

Numbers k such that antisigma(k) = antisigma(k+1), where antisigma(k) = the sum of the nondivisors of k that are between 1 and k. For example, antisigma(5) = 2 + 3 + 4 = 9; antisigma(6) = 4 + 5 = 9, so 5 is a term of the sequence. - Joseph L. Pe, Oct 22 2002

The next term, if it exists, must be greater than 5*10^8. - Martin Fuller, May 06 2007

a(5), if it exists, is greater than 10^13. - Giovanni Resta, Jul 30 2013

No other terms < 2.7x10^15. - Jud McCranie, Jul 27 2025

Crossrefs

Cf. A024816.

Programs

Mathematica

h[n_] := (n (n + 1)/2) - DivisorSigma[1, n]; Select[Range[10^6], h[ # ] == h[ # + 1] &] (* Joseph L. Pe, Oct 22 2002 *)
lst = {}; a = b = 1; Do[ a = b; b = DivisorSigma[1, n]; If[a + n == b, Print[n]; AppendTo[lst, n]], {n, 2^31}] (* Robert G. Wilson v, Jun 02 2007 *)

Extensions

a(5) from Martin Fuller, May 06 2007

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 31 2007