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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

Table of n, a(n) for n=1..5.

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: A243235 A145530 * A076629 A052027 A109514 A022918

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 Plewe, May 31 2007

STATUS

approved

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.