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 A227610 Number of ways 1/n can be expressed as the sum of three distinct unit fractions: 1/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z. 9
 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 ErdÅ‘s and Straus. LINKS Jud McCranie, Table of n, a(n) for n = 1..500 Christian Elsholtz, Sums Of k Unit Fractions, Trans. Amer. Math. Soc. 353 (2001), 3209-3227. David Eppstein, Algorithms for Egyptian Fractions David Eppstein, Ten Algorithms for Egyptian Fractions, Wolfram Library Archive. Ron Knott, Egyptian Fractions 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. Cf. A347566, A347569. 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 January 20 10:09 EST 2022. Contains 350471 sequences. (Running on oeis4.)