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 A223612 #35 Sep 11 2023 01:54:37 %S A223612 1312,29824,8341504,134029312,34356723712 %N A223612 Numbers k whose abundance is 22: sigma(k) - 2*k = 22. %C A223612 Suggested by _N. J. A. Sloane_ and _Robert G. Wilson v_. %C A223612 a(6) > 10^12. %C A223612 a(6) > 10^13. - _Giovanni Resta_, Mar 29 2013 %C A223612 a(6) > 10^18. - _Hiroaki Yamanouchi_, Aug 23 2018 %C A223612 Any term x of this sequence can be combined with any term y of A223606 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. [Proof: If x = a(n) and y = A223606(m), then sigma(x) = 2x+22 and sigma(y) = 2y-22. Thus, sigma(x)+sigma(y) = (2x+22)+(2y-22) = 2x+2y = 2(x+y), which implies that (sigma(x)+sigma(y))/(x+y) = 2(x+y)/(x+y) = 2.] - _Timothy L. Tiffin_, Sep 13 2016 %C A223612 a(6) <= 2361183240644548624384. Every number of the form 2^(j-1)*(2^j - 23), where 2^j - 23 is prime, is a term. - _Jon E. Schoenfield_, Jun 02 2019 %e A223612 For k = 34356723712, sigma(k) - 2*k = 22. %t A223612 Select[Range[1, 10^6], DivisorSigma[1, #] - 2 # == 22 &] (* _Vincenzo Librandi_, Sep 14 2016 *) %o A223612 (PARI) for(n=1, 10^8, if(sigma(n)-2*n==22, print1(n ", "))) %o A223612 (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 22]; // _Vincenzo Librandi_, Sep 14 2016 %Y A223612 Cf. A000203, A033880, A223606 (deficiency 22). %K A223612 nonn,more %O A223612 1,1 %A A223612 _Donovan Johnson_, Mar 23 2013 %E A223612 Name edited by _Timothy L. Tiffin_, Sep 10 2023