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 A085829 #17 Jun 10 2018 10:49:18
%S A085829 1,4,15,42,120,336,930,2548,6930,18870,51300,139440,379080,1030484,
%T A085829 2801202,7614530,20698132,56264040,152941824,415739030,1130096128,
%U A085829 3071920000,8350344420,22698590508,61701166395,167721158286,455913379324,1239301050624,3368769533514
%N A085829 a(n) = least k such that the average number of divisors of {1..k} is >= n.
%C A085829 Does a(n+1)/a(n) converge to e?
%C A085829 Since the total number of divisors of {1..k} (see A006218) is k * (log(k) + 2*gamma - 1) + O(sqrt(k)), the average number of divisors of {1..k} approaches (log(k) + 2*gamma - 1). Since log(a(n)) + 2*gamma - 1 approaches n, a(n+1)/a(n) approaches e. - _Jon E. Schoenfield_, Aug 13 2007
%D A085829 Julian Havil, "Gamma: Exploring Euler's Constant", Princeton University Press, Princeton and Oxford, pp. 112-113, 2003.
%H A085829 Donovan Johnson, <a href="/A085829/b085829.txt">Table of n, a(n) for n = 1..40</a> (first 36 terms from Jon E. Schoenfield)
%e A085829 a(20) = 415739030 because the average number of divisors of {1..415739030} is >= 20.
%t A085829 s = 0; k = 1; Do[ While[s = s + DivisorSigma[0, k]; s < k*n, k++ ]; Print[k]; k++, {n, 1, 20}]
%o A085829 (PARI) A085829(n) = {local(s,k);s=1;k=1;while(s<k*n,k++;s=s+numdiv(k));k} \\ _Michael B. Porter_, Oct 23 2009
%Y A085829 Cf. A050226, A057494, A085567, A006218.
%K A085829 nonn,nice
%O A085829 1,2
%A A085829 _Robert G. Wilson v_, Jul 07 2003
%E A085829 Edited by _Don Reble_, Nov 06 2005
%E A085829 More terms from _Jon E. Schoenfield_, Aug 13 2007