This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A004194 #24 Apr 11 2024 16:44:54
%S A004194 3,10,21,28,36,57,42,70,79,96,62,160,59,136,196,128,73,211,80,292,245,
%T A004194 157,93,366,156,174,230,340,106,497,90,269,322,211,453,538,85,216,378,
%U A004194 604,121,623,104,473,648,204,135,706,227,437,387,467,125,601,561,783,385
%N A004194 Number of partitions of 1/n into 3 reciprocals of positive integers.
%C A004194 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.
%C A004194 See A073101 for the 4/n conjecture due to Erdős and Straus.
%H A004194 Justus Springer, <a href="/A004194/b004194.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..100 from Robert G. Wilson)
%H A004194 K. S. Brown, <a href="http://www.mathpages.com/home/kmath332.htm">Unit Fraction Partitions</a>
%H A004194 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%t A004194 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 *)
%o A004194 (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
%Y A004194 Cf. A227610, A226641, A226642, A192787, A226644, A226645, A226646.
%K A004194 nonn
%O A004194 1,1
%A A004194 Scott Aaronson (philomath(AT)voicenet.com)
%E A004194 More terms from _David W. Wilson_, Aug 15 1996