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 A369333 #15 Apr 04 2024 10:03:38
%S A369333 72,144,168,360,450,480,576,864,990,1152,1200,1344,1404,1568,1600,
%T A369333 1800,1944,2040,2160,2520,2646,2880,3150,3360,3600,3780,3840,3888,
%U A369333 4050,4536,4608,4800,5184,5400,5520,5880,5940,6720,6912,7056,7200,7350,7800,7920,7938,8550,8640,8694,8712,8976,9000,9216,9408,9450,9504,9600,9720,10416,10752,11232,11550,11760
%N A369333 Positive integers m such that there exist distinct pairs (a,b) and (c,d) with a <= b, c <= d, and m = a*b*(c+d) = (a+b)*c*d.
%C A369333 Such numbers m correspond to pairs of equal Egyptian fractions of length 2, since a*b*(c+d) = (a+b)*c*d is equivalent to 1/a + 1/b = 1/c + 1/d.
%C A369333 Numbers of the form t * k^3, where t is a term of A369334 and k is a positive integer.
%C A369333 If m belongs to this sequence, then so does m*k^3 for any positive integer k.
%e A369333 72 is a term since 72 = 3*3*(2+6) = (3+3)*2*6.
%o A369333 (PARI) { find_abcd(m) = my(r); fordiv(m,a, if(2*a*a>m, break); fordiv(m\a,b, if(4*a^2*b^2 > m*(a+b), break); if(b<a || m%(a+b), next); if(a*b*(a+b)==m, next); r=select(x->denominator(x)==1, nfroots(,x^2 - m\a\b*x + m\(a+b))); if(#r==1, r=[r[1],r[1]]); if(#r==2, return([a,b,r[1],r[2]])); )); []; }
%Y A369333 Cf. A088915, A369334, A371721.
%K A369333 nonn
%O A369333 1,1
%A A369333 _Max Alekseyev_, Jan 20 2024