

A004194


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


14



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 ErdÅ‘s and Straus.


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..100
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=t1/a; for(b=max(1\t1+1, a), 2\t1, c=1/(t11/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: A196166 A073604 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



