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Number of ways to express 2/n as Egyptian fractions in just three terms; i.e., 2/n = 1/x + 1/y + 1/z satisfying 1<=x<=y<=z.
6

%I #22 May 01 2020 03:17:52

%S 1,3,8,10,12,21,17,28,26,36,25,57,20,42,81,70,25,79,32,96,86,62,42,

%T 160,53,59,89,136,33,196,37,128,103,73,185,211,32,80,160,292,40,245,

%U 40,157,235,93,60,366,85,156,147,174,42,230,223,340,143,106,76,497,34,90,331,269,206,322,50,211,175,453,72,538,37,85,332,216,260,378,69,604,167,121,79,623,204,104,203,473,59,648,253,204,166,135,318,706,46,227,427,437

%N Number of ways to express 2/n as Egyptian fractions in just three terms; i.e., 2/n = 1/x + 1/y + 1/z satisfying 1<=x<=y<=z.

%H Daniel Leary, <a href="/A226641/b226641.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%t a[n_] := Length@ Solve[ 2/n == 1/x + 1/y + 1/z && 1 <= x <= y <= z, {x, y, z}, Integers]; Array[a, 70]

%Y Cf. A227611, A004194, A226642, A192787, A226644, A226645, A226646.

%Y See A073101 for the 4/n conjecture due to Erdős and Straus.

%K nonn

%O 1,2

%A _Allan C. Wechsler_ and _Robert G. Wilson v_, Aug 17 2013