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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
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

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Last modified June 24 09:22 EDT 2024. Contains 373674 sequences. (Running on oeis4.)