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 A316291 #7 Nov 12 2018 15:45:10 %S A316291 6,20,28,30,40,48,60,66,72,80,84,88,90,96,104,120,126,132,140,144,150, %T A316291 156,160,168,176,180,192,196,198,200,204,208,210,216,220,224,228,234, %U A316291 240,252,260,264 %N A316291 Common denominators of all Egyptian fraction representations of unity (EFROUs) such that replacing two terms with their sum never results in another EFROU. %C A316291 The relevant EFROUs serve as generators, general EFROUs arising by repeatedly replacing terms 1/a with 1/b + 1/c. a(b+c)=bc requires taking b=D(B+C)B and c=D(B+C)C, where B,C|a, gcd(B,C)=1 and D=a/BC. %e A316291 For 6, 1 = 1/2 + 1/3 + 1/6 (combining 1/3 + 1/6 would duplicate 1/2). For 20, 1 = 1/2 + 1/4 + 1/5 + 1/20. Observe that 1 = 1/2 + 1/3 + 1/12 + 1/20 + 1/30 has common denominator 60 even though 1/60 itself does not appear as a summand; since also 1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/12 + 1/30, uniqueness fails for the relevant EFROU, the first such example. %K A316291 nonn %O A316291 1,1 %A A316291 _David V. Feldman_, Jun 28 2018