This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A050507 #34 Jul 28 2025 06:19:03 %S A050507 434,8575,8825 %N A050507 Solutions to sigma(x)+2=sigma(x+2) other than the smaller of twin primes. %C A050507 This sequence together with A001359 gives the solutions of sigma(x)+2 = sigma(x+2). %C A050507 No others < 4.29*10^9. %C A050507 No others < 5*10^10. - _Charles R Greathouse IV_, Oct 19 2010 %C A050507 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 %C A050507 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 %C A050507 a(4) > 10^13, if it exists. - _Giovanni Resta_, Dec 12 2019 %C A050507 No more terms < 2.7*10^15. - _Jud McCranie_, Jul 27 2025 %D A050507 Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, 2004, chapter B13, p. 104. %D A050507 R. Sivaramakrishnan, Classical Theory of Arithmetical Functions, M. Dekker Inc., New York-Basel, 1989, p. 81, Problem 12. %H A050507 Pentti Haukkanen, <a href="https://www.researchgate.net/publication/282603270_SOME_COMPUTATIONAL_RESULTS_CONCERNING_THE_DIVISOR_FUNCTIONS_dn_AND_SIGMAn">Some computational results concerning the divisor functions d(n) and sigma(n)</a>, The Mathematics Student, Vol. 62, Nos. 1-4 (1993), pp. 166-168. %H A050507 Andrzej Makowski <a href="https://doi.org/10.2307/2310107">On Some Equations Involving Functions phi(n) and sigma(n)</a>, The American Mathematical Monthly, Vol. 67, No. 7 (1960), pp. 668-670. %e A050507 sigma(434)+2=770=sigma(434+2), so 434 is in the sequence. %t A050507 Select[Range[10000], CompositeQ[#] && DivisorSigma[1, #] + 2 == DivisorSigma[1, # + 2] &] (* _Amiram Eldar_, Dec 28 2018 *) %o A050507 (PARI) is(n)=sigma(n+2)==sigma(n)+2&&!isprime(n) \\ _Charles R Greathouse IV_, Feb 13 2013 %Y A050507 Cf. A000203, A001359, A054799. %K A050507 nonn,bref,more %O A050507 1,1 %A A050507 _Jud McCranie_, Dec 27 1999