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 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 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: 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

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)