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 A177734 #23 Apr 04 2025 14:34:56 %S A177734 22,24,102728,1011849771855214912968404217247,168,288,848874360,528, %T A177734 695552,886725671,50641,1680,2359785,10776888210,414839198, %U A177734 42176361744,226972,4488,9094138358932,5328,6240 %N A177734 Largest k such that prime(n) divides the numerator of the k-th harmonic number (=A001008(k)). %C A177734 For p = prime(n), Boyd defines J_p to be the set of numbers k such that p divides A001008(k). This sequence gives the largest element of J_p. The smallest element of J_p is given by A072984. The size of J_p is given by A092103. %C A177734 Term a(23) is too large to include, see b-file. - _Max Alekseyev_, Apr 04 2025 %H A177734 Max Alekseyev, <a href="/A177734/b177734.txt">Table of n, a(n) for n = 2..220</a> %H A177734 David W. Boyd, <a href="http://www.emis.de/journals/EM/expmath/volumes/3/3.html">A p-adic study of the partial sums of the harmonic series</a>, Experimental Math., Vol. 3 (1994), No. 4, 287-302. [WARNING: Table 2 contains miscalculations for p=19, 47, 59, ... - _Max Alekseyev_, Feb 10 2016] %H A177734 Leonardo Carofiglio, Giacomo Cherubini, and Alessandro Gambini, <a href="https://arxiv.org/abs/2503.15714">On Eswarathasan--Levine and Boyd's conjectures for harmonic numbers</a>, arXiv:2503.15714 [math.NT], 2025. %F A177734 For p = prime(n) in A092101, a(n) = p^2 - 1. %Y A177734 Cf. A072984, A092103, A092193. %K A177734 hard,nonn %O A177734 2,1 %A A177734 _Max Alekseyev_, May 12 2010 %E A177734 a(5) computed by Boyd. %E A177734 a(8)-a(22) from _Max Alekseyev_, Oct 23 2012