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%I #26 Oct 19 2017 03:14:35
%S 2,3,5,11,17,79,733,27539
%N a(n) = least denominator Y of the proper fractions X/Y which need n or more terms as an Egyptian fraction.
%C These are the simplest proper fractions requiring n parts as an Egyptian fraction, where "simplest" means smallest denominator and the smallest numerator breaks ties: 1/2, 2/3, 4/5, 8/11, 16/17, 77/79, 732/733, ...
%C Checking just (p-1)/p for prime p finds no example requiring 9 parts for p <= 800399: see "results-single" in the github link. - _Hugo van der Sanden_, Feb 28 2015
%D R. K. Guy, Unsolved Problems in Number Theory, D11
%H David Eppstein, <a href="http://library.wolfram.com/infocenter/Articles/2926/">Ten Algorithms for Egyptian Fractions</a>
%H Hugo van der Sanden, <a href="https://github.com/hvds/seq/tree/master/least_eg">code and results</a> on github.
%e 27538/27539 is the simplest rational that cannot be expressed as the sum of 7 or fewer distinct unit fractions. That is, no rational p/q requires 8 or more with 0 < p/q < 1, and either q < 27539 or (q = 27539 and p < 27538). - _Hugo van der Sanden_, Sep 14 2010
%Y See A097049 for numerators.
%K nonn,more,frac,nice
%O 1,1
%A _Ed Pegg Jr_ and _Don Reble_, Jul 21 2004
%E a(8) from _Hugo van der Sanden_, Sep 14 2010
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