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 A273235 #17 May 21 2016 23:41:15 %S A273235 3,10,17,28,27,43,44,69,68,58,97,97,125,164,201,185,162,254,263,313, %T A273235 491,434,466,417,309,358,510,633,935,1148,454 %N A273235 Number of Ramanujan's largely composite numbers having prime(n) as the greatest prime divisor. %C A273235 Theorem. The sequence is unbounded. %C A273235 Proof. Since the sequence of highly composite numbers (A002182) is a subsequence of this sequence, it is sufficient to prove that the number M_n of highly composite numbers with the maximal prime divisor p_n is unbounded. Let N be a large highly composite number. Then for the greatest prime divisor p_N of N we have [Erdos] p_N=O(log N). So for all N<=x, p_N=O(log x). %C A273235 If M_n=O(1), then the number of all highly composite numbers <=x is O(p_n)=O(log x). However, Erdos [Erdos] proved that this number is more than (log x)^(1+c) for a certain c>0. %C A273235 So we have a contradiction. This means that M_n and this sequence are unbound. QED %H A273235 P. Erdős, <a href="https://www.renyi.hu/~p_erdos/1944-04.pdf">On Highly composite numbers</a>, J. London Math. Soc. 19 (1944), 130--133 MR7,145d; Zentralblatt 61,79. %Y A273235 Cf. A067128, A273015, A273016, A273018, A273057. %K A273235 nonn,more %O A273235 1,1 %A A273235 _Vladimir Shevelev_ and _Peter J. C. Moses_, May 18 2016