The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A050507 Solutions to sigma(x)+2=sigma(x+2) other than the smaller of twin primes. 6
 434, 8575, 8825 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence together with A001359 gives the solutions of sigma(x)+2 = sigma(x+2). No others < 4.29*10^9. No others < 5*10^10. - Charles R Greathouse IV, Oct 19 2010 They are also the solutions of A001065(x) = A001065(x+2), where A001065(n) is the sum of proper divisors of n. - Michel Marcus, Nov 14 2014 Makowski found these 3 solutions and verified that there are none others with x <= 9998. Haukkanen extended the bound to 2*10^8. - Amiram Eldar, Dec 28 2018 a(4) > 10^13, if it exists. - Giovanni Resta, Dec 12 2019 REFERENCES Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, 2004, chapter B13, p. 104. R. Sivaramakrishnan, Classical Theory of Arithmetical Functions, M. Dekker Inc., New York-Basel, 1989, p. 81, Problem 12. LINKS Table of n, a(n) for n=1..3. Pentti Haukkanen, Some computational results concerning the divisor functions d(n) and sigma(n), The Mathematics Student, Vol. 62, Nos. 1-4 (1993), pp. 166-168. Andrzej Makowski On Some Equations Involving Functions phi(n) and sigma(n), The American Mathematical Monthly, Vol. 67, No. 7 (1960), pp. 668-670. EXAMPLE sigma(434)+2=770=sigma(434+2), so 434 is in the sequence. MATHEMATICA Select[Range[10000], CompositeQ[#] && DivisorSigma[1, #] + 2 == DivisorSigma[1, # + 2] &] (* Amiram Eldar, Dec 28 2018 *) PROG (PARI) is(n)=sigma(n+2)==sigma(n)+2&&!isprime(n) \\ Charles R Greathouse IV, Feb 13 2013 CROSSREFS Cf. A000203, A001359, A054799. Sequence in context: A219033 A237386 A259294 * A145318 A054987 A054905 Adjacent sequences: A050504 A050505 A050506 * A050508 A050509 A050510 KEYWORD nonn,bref,more AUTHOR Jud McCranie, Dec 27 1999 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 18 15:50 EDT 2024. Contains 372664 sequences. (Running on oeis4.)