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 A227610 Number of ways to express 1/n as Egyptian fractions in just three terms: 1/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z. 4
 1, 6, 15, 22, 30, 45, 36, 62, 69, 84, 56, 142, 53, 124, 178, 118, 67, 191, 74, 274, 227, 145, 87, 342, 146, 162, 216, 322, 100, 461, 84, 257, 304, 199, 435, 508, 79, 204, 360, 580, 115, 587, 98, 455, 618, 192, 129, 676, 217, 417, 369, 449, 119, 573, 543, 759, 367, 240, 166, 1236, 102, 261, 857, 428, 568, 717, 115, 537, 460, 1018, 155, 1126, 112, 276, 839 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A073101 for the 4/n conjecture due to Erdős and Straus. LINKS Christian Elsholtz, Sums Of k Unit Fractions David Eppstein, Algorithms for Egyptian Fractions David Eppstein, Ten Algorithms for Egyptian Fractions Ron Knott Egyptian Fractions Oakland University The Erdős Number Project Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE a(1)=1 because 1 = 1/2 + 1/3 + 1/6; a(2)=6 because 1/2 = 1/3 + 1/7 + 1/42 = 1/3 + 1/8 + 1/24 = 1/3 + 1/9/ +1/18 = 1/3 + 1/10 + 1/15 = 1/4 + 1/5 + 1/20 = 1/4 + 1/6 + 1/12; a(3)=15 because 1/3 = 1/x = 1/y + 1/z presented as {x,y,z}: {4,13,156}, {4,14,84}, {4,15,60}, {4,16,48}, {4,18,36}, {4,20,30}, {4,21,28}, {5,8,120}, {5,9,45}, {5,10,30}, {5,12,20}, {6,7,42}, {6,8,24}, {6,9,18}, {6,10,15}; etc. MATHEMATICA f[n_] := Length@ Solve[1/n == 1/x + 1/y + 1/z && 0 < x < y < z, {x, y, z}, Integers]; Array[f, 70] CROSSREFS Cf. A002966, A073546. Cf. A227611 (2/n), A075785 (3/n), A073101 (4/n), A075248 (5/n), A227612. Sequence in context: A130178 A100410 A095032 * A238905 A187918 A190747 Adjacent sequences:  A227607 A227608 A227609 * A227611 A227612 A227613 KEYWORD nonn AUTHOR Robert G. Wilson v, Jul 17 2013 STATUS approved

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Last modified August 26 02:19 EDT 2019. Contains 326324 sequences. (Running on oeis4.)