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 A067816 Numbers n such that sigma(n+1) - sigma(n) = n + 1. 11
 1, 5, 8585, 16119, 29886159 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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, 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 LINKS 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 *) CROSSREFS Cf. A024816. Sequence in context: A116140 A243235 A145530 * A076629 A052027 A109514 Adjacent sequences:  A067813 A067814 A067815 * A067817 A067818 A067819 KEYWORD nonn AUTHOR Benoit Cloitre, Feb 08 2002 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 STATUS approved

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Last modified October 17 02:04 EDT 2019. Contains 328106 sequences. (Running on oeis4.)