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 A186129 #17 Sep 08 2022 08:45:55
%S A186129 18,27,32,36,45,48,50,54,63,64,72,75,80,81,90,96,98,99,100,108,112,
%T A186129 117,125,126,128,135,144,147,150,153,160,162,171,175,176,180,189,192,
%U A186129 196,198,200,207,208,216,224,225,234,240,242,243,245,250,252,256,261
%N A186129 Numbers that can be partitioned into four parts s, t, u, v such that s+k = t-k = u*k = v/k for some k > 1.
%C A186129 Equivalently, solutions n to a*(b+1)^2 = b*n with a > b >= 2.
%C A186129 The general rule to obtain such a partition is to start with any number b > 1 and one of its multiples a = k*b (k > 1 and a < n) and let s = a-b, t = a+b, u = a/b and v = a*b.
%C A186129 Sequence appears to be a subsequence of A013929, of A046790, and of A072903.
%D A186129 José Estalella, Ciencia Recreativa. Gustavo Gili - Editor. Barcelona, 1918, pp. 5-6.
%H A186129 Klaus Brockhaus, <a href="/A186129/b186129.txt">Table of n, a(n) for n = 1..1178</a> (terms <= 5000)
%e A186129 18 = 2+6+2+8; for k=2 we have 2+2 = 6-2 = 2*2 = 8/2 = 4, hence 18 is a term.
%e A186129 45 = 8+12+5+20; for k=2 we have 8+2 = 12-2 = 5*2 = 20/2 = 10, hence 45 is a term.
%o A186129 (Magma) [ n: n in [1..300] | exists{ b: b in [2..n] | exists{ a: a in [b+1..n div 4] | n*b eq a*(b+1)^2 } } ]; // _Klaus Brockhaus_, Feb 15 2011
%Y A186129 Cf. A000041, A013929, A046790, A072903.
%K A186129 nonn
%O A186129 1,1
%A A186129 _Manuel Valdivia_, Feb 13 2011