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

1,1

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.

Links

Table of n, a(n) for n=1..42.

Example

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.

Crossrefs

Sequence in context: A308324 A044970 A345910 * A090502 A324649 A324643

Adjacent sequences: A316288 A316289 A316290 * A316292 A316293 A316294

Keyword

nonn

Author

David V. Feldman, Jun 28 2018

Status

approved