1,2

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

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

The next term, if it exists, must be greater than 5*10^8. - Martin Fuller (martin_n_fuller(AT)btinternet.com), May 06 2007

h[n_] := (n (n + 1)/2) - DivisorSigma[1, n]; Select[Range[10^6], h[ # ] == h[ # + 1] &] - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), 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 (rgwv(AT)rgwv.com), Jun 02 2007 *)

Cf. A024816.

Sequence in context: A117711 A116140 A145530 this_sequence A076629 A052027 A109514

Adjacent sequences: A067813 A067814 A067815 this_sequence A067817 A067818 A067819

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 08 2002

a(5) from Martin Fuller (martin_n_fuller(AT)btinternet.com), May 06 2007

Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, May 31 2007