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 A335189 #20 May 26 2020 10:26:52
%S A335189 21,23,43,47,66,68,78,82,86,111,115,119,157,160,164,167,273,287,343,
%T A335189 359,438,442,456,460,507,527,579,581,615,665,813,818,834,839,931,943,
%U A335189 947,959,1082,1090,1111,1119,1140,1148,1248,1288,1333,1340,1346,1354,1360,1367,1592,1640,1641,1679,1807,1847,2034,2067,2069,2163,2190
%N A335189 Numbers L such that there is a prime p <= L for which v_p(H_L - 1) > 0, where v_p(x) is the p-adic valuation of x and H_L is the L-th harmonic number.
%C A335189 For more numbers in this list (up to 10^6), see one of the links below by Krattenthaler and Rivoal. The first few numbers L for which v_p(H_L-1) = 2 (rather than 1) for some prime p <= L are 43, 2034 and 2069 with corresponding primes 7, 13 and 7.
%C A335189 The calculation of v_p(H_L-1) and v_p(H_L) for all primes p <= L is related to some results about the integrality of the Taylor coefficients of mirror maps. See Theorems 3 and 4 in Krattenthaler and Rivoal (2007-2009, 2009) and sequences A007757, A131657, and A131658.
%H A335189 David W. Boyd, <a href="https://doi.org/10.1080/10586458.1994.10504298">A p-adic study of the partial sum of the harmonic series</a>, Experimental Mathematics, 3(4) (1994), 287-302.
%H A335189 Christian Krattenthaler and Tanguy Rivoal, <a href="http://arxiv.org/abs/0709.1432">On the integrality of the Taylor coefficients of mirror maps</a>, arXiv:0709.1432 [math.NT], 2007-2009.
%H A335189 Christian Krattenthaler and Tanguy Rivoal, <a href="https://www.mat.univie.ac.at/~kratt/artikel/H1.html">Supplement 2 to the paper "On the integrality of the Taylor coefficients of mirror maps"</a>, 2007-2009. [This table contains all triplets of numbers (L, p, v_p(H_L - 1)) such that 1 <= L <= 10^6, p prime <= L, and v_p(H_L - 1) > 0.]
%H A335189 Christian Krattenthaler and Tanguy Rivoal, <a href="http://dx.doi.org/10.4310/CNTP.2009.v3.n3.a5">On the integrality of the Taylor coefficients of mirror maps, II</a>, Communications in Number Theory and Physics, Volume 3, Number 3 (2009), 555-591.
%H A335189 Carlo Sanna, <a href="https://doi.org/10.1016/j.jnt.2016.02.020">On the p-adic valuation of harmonic numbers</a>, Journal of Number Theory, 166 (2016), 41-46.
%o A335189 (PARI) h(n) = sum(i=1, n, 1/i);
%o A335189 is(n) = {forprime(p=1, n, if(valuation((numerator(h(n)-1)), p) > 0, return(1))); return(0)};
%o A335189 for(n=1, 1000, if(is(n)==1, print1(n,",")))
%Y A335189 Cf. A007757, A131657, A131658, A268112, A334981.
%K A335189 nonn
%O A335189 1,1
%A A335189 _Petros Hadjicostas_, May 26 2020