OFFSET
2,3
COMMENTS
LINKS
T. D. Noe, Table of n, a(n) for n = 2..1000
Ron Knott, Egyptian Fractions.
Eric Weisstein's World of Mathematics, Egyptian Fraction.
EXAMPLE
a(4)=2 because there are two solutions: 5/4 = 1/1 + 1/5 + 1/20 and 5/4 = 1/1 + 1/6 + 1/12.
MATHEMATICA
m = 5; For[lst = {}; n = 2, n <= 100, n++, cnt = 0; xr = n/m; If[IntegerQ[xr], xMin = xr + 1, xMin = Ceiling[xr]]; If[IntegerQ[3xr], xMax = 3xr - 1, xMax = Floor[3xr]]; For[x = xMin, x <= xMax, x++, yr = 1/(m/n - 1/x); If[IntegerQ[yr], yMin = yr + 1, yMin = Ceiling[yr]]; If[IntegerQ[2yr], yMax = 2yr + 1, yMax = Ceiling[2yr]]; For[y = yMin, y <= yMax, y++, zr = 1/(m/n - 1/x - 1/y); If[y > x && zr > y && IntegerQ[zr], z = zr; cnt++; (*Print[n, " ", x, " ", y, " ", z]*)]]]; AppendTo[lst, cnt]]; lst
f[n_] := Length@ Solve[5/n == 1/x + 1/y + 1/z && 0 < x < y < z, {x, y, z}, Integers]; Array[f, 74] (* Robert G. Wilson v, Jul 17 2013 *)
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
T. D. Noe, Sep 10 2002
STATUS
approved