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 A335254 #10 Jul 25 2024 01:41:11 %S A335254 672,523776,19327369215 %N A335254 Numbers k such that the abundance (A033880) of k is equal to the deficiency (A033879) of k+1. %C A335254 Equivalently, k and k+1 have the same absolute value of abundance (or deficiency) with opposite signs. %C A335254 Equivalently, s(k) + s(k+1) = k + (k+1), where s(k) is the sum of proper divisors of k (A001065). %C A335254 If k is a 3-perfect number (A005820) and k+1 is a prime, then k is in the sequence. Of the 6 known 3-perfect numbers only 672 and 523776 have this property. %C A335254 a(4) > 10^11, if it exists. %C A335254 a(4) > 10^13, if it exists. - _Giovanni Resta_, May 30 2020 %e A335254 672 is a term since A033880(672) = sigma(672) - 2*672 = 2016 - 1344 = 672, and A033879(673) = 2*673 - sigma(673) = 1346 - 674 = 672. %t A335254 ab[n_] := DivisorSigma[1, n] - 2*n; Select[Range[6 * 10^5], ab[#] == -ab[# + 1] &] %Y A335254 Cf. A000203, A001065, A005820, A033879, A033880, A330901, A335253. %K A335254 nonn,hard,bref,more %O A335254 1,1 %A A335254 _Amiram Eldar_, May 28 2020