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.
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
KEYWORD
nonn
AUTHOR
David V. Feldman, Jun 28 2018
STATUS
approved