OFFSET
1,1
COMMENTS
Number of ways to express 1/n as Egyptian fractions in just three terms; i.e., 1/n = 1/x + 1/y + 1/z satisfying 1<=x<=y<=z.
See A073101 for the 4/n conjecture due to Erdős and Straus.
LINKS
Justus Springer, Table of n, a(n) for n = 1..5000 (terms 1..100 from Robert G. Wilson)
K. S. Brown, Unit Fraction Partitions
MATHEMATICA
a[n_] := Length@ Solve[ 1/n == 1/x + 1/y + 1/z && 1 <= x <= y <= z, {x, y, z}, Integers]; Array[a, 70] (* Allan C. Wechsler and Robert G. Wilson v, Aug 17 2013 *)
PROG
(PARI) a(n)=my(t=1/n, t1, s, c); for(a=1\t+1, 3\t, t1=t-1/a; for(b=max(1\t1+1, a), 2\t1, c=1/(t1-1/b); if(denominator(c)==1&&c>=b, s++))); s \\ Charles R Greathouse IV, Jun 12 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott Aaronson (philomath(AT)voicenet.com)
EXTENSIONS
More terms from David W. Wilson, Aug 15 1996
STATUS
approved