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 A227042 #18 Feb 16 2025 08:33:20 %S A227042 1,3,1,2,5,1,5,3,7,1,3,7,4,9,1,7,1,1,5,11,1,4,9,5,11,6,13,1,9,5,11,3, %T A227042 13,7,15,1,5,11,2,13,7,5,8,17,1,11,3,13,7,3,2,17,9,19,1,6,13,7,15,8, %U A227042 17,9,19,10,21,1 %N A227042 Triangle of denominators of harmonic mean of n and m, 1 <= m <= n. %C A227042 See the comments under A227041. a(n,m) gives the denominator of H(n,m) = 2*n*m/(n+m) in lowest terms. %H A227042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicMean.html">Harmonic Mean</a>. %F A227042 a(n,m) = denominator(2*n*m/(n+m)), 1 <= m <= n. %F A227042 a(n,m) = (n+m)/gcd(2*n*m, n+m) = (n+m)/gcd(n+m, 2*m^2), 1 <= m <= n. %e A227042 The triangle of denominators of H(n,m), called a(n,m) begins: %e A227042 n\m 1 2 3 4 5 6 7 8 9 10 11 ... %e A227042 1: 1 %e A227042 2: 3 1 %e A227042 3: 2 5 1 %e A227042 4: 5 3 7 1 %e A227042 5: 3 7 4 9 1 %e A227042 6: 7 1 1 5 11 1 %e A227042 7: 4 9 5 11 6 13 1 %e A227042 8; 9 5 11 3 13 7 15 1 %e A227042 9: 5 11 2 13 7 5 8 17 1 %e A227042 10: 11 3 13 7 3 2 17 9 19 1 %e A227042 11: 6 13 7 15 8 17 9 19 10 21 1 %e A227042 ... %e A227042 For the triangle of the rationals H(n,m) see the example section of A227041. %e A227042 H(4,2) = denominator(16/6) = denominator(8/3) = 3 = 6/gcd(6,8) = 6/2. %Y A227042 Cf. A227041, A026741 (column m=1), A000265 (m=2), A106619 (m=3), A227140(n+8) (m=4), A227108 (m=5), A221918/A221919. %K A227042 nonn,easy,frac,tabl %O A227042 1,2 %A A227042 _Wolfdieter Lang_, Jul 01 2013