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 A320884 #25 Dec 06 2018 03:40:57
%S A320884 45,96,120,225,288,540,640,1080,1200,1920,2160,3888,4000,4500,4608,
%T A320884 5760,6480,7200,8640,9600,10935,16875,18225,25000,25600,27000,28800,
%U A320884 30720,31104,38400,46080,48600,69984,75000,81000,91125,97200,102400,112500,115200,164025,184320
%N A320884 5-smooth numbers of the form (ab+1)(ac+1), a > b > c > 0.
%C A320884 Corvaja & Zannier show that there are only finitely many p-smooth terms in A180045, for any prime p. This sequences lists these terms for p = 5, and is therefore finite.
%C A320884 Can someone prove that a(163) = 3327916660110655488000000000 = (16775191*16038089 + 1)(16775191*737369 + 1) = 2^42 * 3^18 * 5^9 is the last term? - _M. F. Hasler_, Nov 19 2018
%C A320884 If a(164) exists it's larger than 10^60. - _David A. Corneth_, Nov 20 2018
%H A320884 M. F. Hasler, <a href="/A320884/b320884.txt">Table of n, a(n) for n = 1..163</a> (all terms up to 10^30, and up to 10^60 according to _David A. Corneth_)
%H A320884 P. Corvaja and U. Zannier, <a href="https://doi.org/10.1090/S0002-9939-02-06771-0">On the greatest prime factor of (ab+1)(ac+1)</a>, Proceedings of the American Mathematical Society 131 (2003), pp. 1705-1709. See also <a href="https://arxiv.org/abs/math/0205136">arXiv:math/0205136 [math.NT]</a>, 2002.
%F A320884 Intersection of A051037 and A180045.
%t A320884 (* This is only a recomputation of the existing data section. *)
%t A320884 jmax = 12; kmax = 8; lmax = 5; max = 200000;
%t A320884 r[j_, k_, l_] := r[j, k, l] = If[2^j*3^k*5^l > max, Return[False], Reduce[a > b > c > 0 && (a b + 1)(a c + 1) == 2^j*3^k*5^l, {a, b, c}, Integers]];
%t A320884 rea = Reap[Do[rr = r[j, k, l]; If[rr =!= False, res = {j, k, l, 2^j*3^k*5^l}; Print[res]; Sow[res]], {j, 0, jmax}, {k, 0, kmax}, {l, 0, lmax}]][[2, 1]] //Union;
%t A320884 Print["min = ", Min /@ Transpose[rea], " max = ", Max /@ Transpose[rea]];
%t A320884 Sort[rea[[All, 4]]] (* _Jean-François Alcover_, Dec 05 2018 *)
%o A320884 (PARI) is_A320884(n)={vecmax(factor(n,5)[,1])<6 && is_A180045(n)}
%o A320884 A320884=select( is_A180045, A051037_list(1e30))
%Y A320884 Cf. A180045 (numbers (ab+1)(ac+1), a>b>c), A320883 (subsequence of 3-smooth terms), A051037 (5-smooth numbers).
%K A320884 nonn,fini
%O A320884 1,1
%A A320884 _M. F. Hasler_, Nov 19 2018