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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

Table of n, a(n) for n=1..75.

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

Index entries for sequences related to Egyptian fractions

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.)