A316291 Common denominators of all Egyptian fraction representations of unity (EFROUs) such that replacing two terms with their sum never results in another EFROU.

6, 20, 28, 30, 40, 48, 60, 66, 72, 80, 84, 88, 90, 96, 104, 120, 126, 132, 140, 144, 150, 156, 160, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240, 252, 260, 264

Offset: 1

Author

David V. Feldman, Jun 28 2018

Keywords

• nonn

Comments

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.

Examples

			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.