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 A353538 #17 Sep 04 2023 10:25:58 %S A353538 44,63,75,104,135,164,188,189,195,224,230,231,255,284,285,315,344,374, %T A353538 375,404,405,434,435,440,441,464,494,495,524,567,584,675,692,735,764, %U A353538 819,824,825,854,855,944,945,975,1034,1035,1070,1071,1124,1155,1196,1215,1274 %N A353538 Numbers k such that k and k+1 both have an abundancy index that is larger than Pi^2/6. %C A353538 The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 3, 43, 399, 4292, 41306, 413310, 4155925, 414963651, 4149603572, ... %C A353538 Apparently, the asymptotic density of this sequence is 0.04149... %H A353538 Amiram Eldar, <a href="/A353538/b353538.txt">Table of n, a(n) for n = 1..10000</a> %e A353538 44 is a term since sigma(44)/44 = 84/44 = 1.909... and sigma(45)/45 = 78/45 = 1.733... are both larger than Pi^2/6 = 1.644... . %t A353538 q[n_] := DivisorSigma[-1, n] > Pi^2/6; Select[Range[1300], q[#] && q[# + 1] &] %o A353538 (PARI) isok(k) = ((sigma(k)/k) > Pi^2/6) && ((sigma(k+1)/(k+1)) > Pi^2/6); \\ _Michel Marcus_, Apr 25 2022 %Y A353538 Cf. A000203, A013661. %Y A353538 Subsequence of A353537. %Y A353538 Subsequences: A096399, A353539, A353540, A353541. %K A353538 nonn %O A353538 1,1 %A A353538 _Amiram Eldar_, Apr 25 2022