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 A353537 #14 Apr 26 2022 04:45:52 %S A353537 4,6,8,10,12,14,16,18,20,24,28,30,32,36,40,42,44,45,48,50,52,54,56,60, %T A353537 63,64,66,68,70,72,75,76,78,80,84,88,90,92,96,98,100,102,104,105,108, %U A353537 110,112,114,116,120,124,126,128,130,132,135,136,138,140,144,148,150 %N A353537 Numbers whose abundancy index is larger than Pi^2/6. %C A353537 The abundancy index of a number k is sigma(k)/k, where sigma is the sum of divisors function (A000203). %C A353537 Pi^2/6 (A013661) is the asymptotic mean of the abundancy indices of the positive integers. %C A353537 The least odd term is 45 and the least term that is coprime to 6 is 25025. %C A353537 Davenport (1933) proved that sigma(k)/k possesses a continuous distribution function and that the asymptotic density of numbers with abundancy index that is larger than x exists for all x > 1 and is a continuous function of x. Therefore, this sequence has an asymptotic density. %C A353537 The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 4, 41, 436, 4258, 42928, 428557, 4286145, 42864566, 428585795, 4286368677, 42861854540, ... Apparently, the asymptotic density is 0.4286... which means that the distribution of the abundancy indices is skewed with a positive nonparametric skew. %D A353537 Harold Davenport, Über numeri abundantes, Sitzungsberichte der Preußischen Akademie der Wissenschaften, phys.-math. Klasse, No. 6 (1933), pp. 830-837. %H A353537 Amiram Eldar, <a href="/A353537/b353537.txt">Table of n, a(n) for n = 1..10000</a> %H A353537 Wikipedia, <a href="https://en.wikipedia.org/wiki/Nonparametric_skew">Nonparametric skew</a>. %e A353537 4 is a term since sigma(4)/4 = 7/4 = 1.75 > Pi^2/6 = 1.644... %t A353537 Select[Range[150], DivisorSigma[-1, #] > Pi^2/6 &] %o A353537 (PARI) isok(k) = sigma(k)/k > Pi^2/6; \\ _Michel Marcus_, Apr 25 2022 %Y A353537 Cf. A000203, A005100, A013661, A017665, A017666, A072355, A302991, A330899. %Y A353537 A005101 is a subsequence. %Y A353537 Subsequences: A353538, A353539, A353540, A353541. %K A353537 nonn %O A353537 1,1 %A A353537 _Amiram Eldar_, Apr 25 2022