A004194 Number of partitions of 1/n into 3 reciprocals of positive integers.

3, 10, 21, 28, 36, 57, 42, 70, 79, 96, 62, 160, 59, 136, 196, 128, 73, 211, 80, 292, 245, 157, 93, 366, 156, 174, 230, 340, 106, 497, 90, 269, 322, 211, 453, 538, 85, 216, 378, 604, 121, 623, 104, 473, 648, 204, 135, 706, 227, 437, 387, 467, 125, 601, 561, 783, 385

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

Index entries for sequences related to Egyptian fractions

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

Cf. A227610, A226641, A226642, A192787, A226644, A226645, A226646.

Sequence in context: A073604 A370032 A210990 * A097590 A289183 A194141

Adjacent sequences: A004191 A004192 A004193 * A004195 A004196 A004197

Keyword

nonn

Author

Scott Aaronson (philomath(AT)voicenet.com)

Extensions

More terms from David W. Wilson, Aug 15 1996

Status

approved