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A316291 Common denominators of all Egyptian fraction representations of unity (EFROUs) such that replacing two terms with their sum never results in another EFROU. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 7 12:03 EDT 2022. Contains 357271 sequences. (Running on oeis4.)