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 A007622 M4096 #32 Feb 16 2025 08:32:31
%S A007622 6,12,20,30,42,56,60,72,90,105,110,132,140,156,168,182,210,240,252,
%T A007622 272,280,306,342,360,380,420,462,495,504,506,552,600,630,650,660,702,
%U A007622 756,812,840,858,870,930,992,1056,1092,1122,1190,1260,1320,1332
%N A007622 Consider Leibniz's harmonic triangle (A003506) and look at the non-boundary terms. Sequence gives numbers appearing in denominators, sorted.
%C A007622 No term is prime, about 80% are abundant, but the first few deficient are: 105, 110, 182, 495, 506, 1365, 1406, 1892, 2162, 2756, 2907, 3422, 3782, 4556, 5313, .... - _Robert G. Wilson v_, Aug 16 2010
%C A007622 A002943 = (6, 20, 42, 72, 110, 156, 210, 272, 342, 420, 506, 600, 702, ...) is a subsequence: indeed, this is every second denominator of the first differences of the sequence 1/n. - _M. F. Hasler_, Oct 11 2015
%D A007622 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 83, Problem 25.
%D A007622 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007622 D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 35.
%H A007622 Robert G. Wilson v, <a href="/A007622/b007622.txt">Table of n, a(n) for n = 1..1217</a>.
%H A007622 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeibnizHarmonicTriangle.html">Leibniz Harmonic Triangle.</a>
%t A007622 L[n_, 1] := 1/n; L[n_, m_] := L[n, m] = L[n - 1, m - 1] - L[n, m - 1]; Take[ Union[ Flatten[ Table[ 1/L[n, m], {n, 3, 150}, {m, 2, Floor[n/2 + .5]}]]], 65]
%t A007622 t[n_, k_] := Denominator[n!*k!/(n + k + 1)!]; Take[ DeleteDuplicates@ Rest@ Sort@ Flatten@ Table[t[n - k, k], {n, 2, 150}, {k, n/2 + 1}], 65] (* _Robert G. Wilson v_, Jun 12 2014 *)
%K A007622 nonn
%O A007622 1,1
%A A007622 _N. J. A. Sloane_, _Robert G. Wilson v_, _Mira Bernstein_
%E A007622 More terms from Larry Reeves (larryr(AT)acm.org), Jul 25 2000. Rechecked Jun 27 2003.