A075785 Number of ways to express 3/n as Egyptian fractions in just three terms.

0, 1, 1, 3, 7, 6, 6, 16, 15, 15, 13, 22, 8, 27, 30, 26, 21, 45, 8, 59, 36, 29, 20, 62, 32, 45, 69, 67, 27, 84, 14, 59, 56, 44, 129, 142, 15, 45, 53, 130, 31, 124, 21, 131, 178, 40, 29, 118, 38, 88, 67, 102, 43, 191, 102, 180, 74, 57, 43, 274, 21, 75, 227, 86, 144, 145, 23, 121, 87

Offset: 1

Author

Robert G. Wilson v, Aug 18 2002

Keywords

• nonn

Links

• Christian Elsholtz, Sums Of k Unit Fractions
• David Eppstein, Algorithms for Egyptian Fractions

Crossrefs

Cf. A073101, A347566, A347569.

Programs

Mathematica

Needs["MyOwn`Egypt`"]; Table[ Length[ EgyptianFraction[3/n, Method -> Lexicographic, MaxTerms -> 3, MinTerms -> 3, Duplicates -> Disallow, OutputFormat -> Plain]], {n, 5, 70}]
f[n_] := Length@ Solve[3/n == 1/x + 1/y + 1/z && 0 < x < y < z, {x, y, z}, Integers]; Array[f, 69] (* Robert G. Wilson v, Jul 17 2013 *)