A226645 Number of ways to express 6/n as Egyptian fractions in just three terms; i.e., 6/n = 1/x + 1/y + 1/z satisfying 1<=x<=y<=z.

0, 1, 1, 3, 3, 3, 1, 6, 8, 10, 7, 10, 1, 9, 12, 20, 8, 21, 2, 21, 17, 16, 11, 28, 7, 11, 26, 33, 9, 36, 3, 31, 25, 24, 60, 57, 2, 11, 20, 68, 10, 42, 6, 35, 81, 23, 15, 70, 10, 37, 25, 51, 14, 79, 33, 76, 32, 30, 20, 96, 2, 17, 86, 65, 48, 62, 9, 50, 42, 138, 35, 160, 2, 18, 53, 51, 52, 59, 8, 142, 89, 34, 23, 136, 37, 24, 33, 140, 23, 196, 30, 46, 37, 32, 75, 128, 5, 43, 103, 98

Offset: 1

Author

Allan C. Wechsler and Robert G. Wilson v, Aug 17 2013

Keywords

• nonn

Comments

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

Links

• Daniel Leary, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A226640, A004194, A226642, A192787, A226644, A226646.

Programs

Mathematica

a[n_] := Length@ Solve[ 6/n == 1/x + 1/y + 1/z && 1 <= x <= y <= z, {x, y, z}, Integers]; Array[a, 70]