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%I #7 Nov 12 2018 15:45:10
%S 6,20,28,30,40,48,60,66,72,80,84,88,90,96,104,120,126,132,140,144,150,
%T 156,160,168,176,180,192,196,198,200,204,208,210,216,220,224,228,234,
%U 240,252,260,264
%N Common denominators of all Egyptian fraction representations of unity (EFROUs) such that replacing two terms with their sum never results in another EFROU.
%C 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 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 nonn
%O 1,1
%A _David V. Feldman_, Jun 28 2018
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