

A050507


Solutions to sigma(x)+2=sigma(x+2) other than the smaller of twin primes.


6




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.
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


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed. New York: SpringerVerlag, 2004, chapter B13, p. 104.
R. Sivaramakrishnan, Classical Theory of Arithmetical Functions, M. Dekker Inc., New YorkBasel, 1989, p. 81, Problem 12.


LINKS



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



CROSSREFS



KEYWORD

nonn,bref,more


AUTHOR



STATUS

approved



