

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



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



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



