

A067816


Numbers n such that sigma(n+1)  sigma(n) = n + 1.


11




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: A116140 A243235 A145530 * A076629 A052027 A109514
Adjacent sequences: A067813 A067814 A067815 * A067817 A067818 A067819


KEYWORD

nonn,more


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



