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%I #17 Mar 31 2021 10:46:15
%S 28,45,96,120,126,175,225,280,288,336,378,441,540,560,630,640,672,
%T 1080,1200,1225,1470,1680,1701,1792,1920,2016,2160,2520,2835,3136,
%U 3888,3969,4000,4200,4500,4608,5250,5600,5760,6480,6860,7200,7840,7875,8400,8640,8960
%N 7-smooth numbers of the form (ab+1)*(ac+1), a > b > c > 0.
%C Sequence is finite (see comments at A320884).
%H David A. Corneth, <a href="/A332764/b332764.txt">Table of n, a(n) for n = 1..1072</a>
%F Intersection of A002473 and A180045.
%t Block[{nn = 9000, nm, m}, nm = Ceiling[(Sqrt[8 nn + 1] - 3)/4]; Union@ Reap[Do[If[a > b > c > 0, Set[m, (a b + 1) (a c + 1)]; If[And[m <= nn, FactorInteger[m][[-1, 1]] <= 7 ], Sow[m]]], {a, nm}, {b, a - 1}, {c, b - 1}]][[2, 1]]] (* _Michael De Vlieger_, Feb 25 2020, after _Jean-François Alcover_ at A180045 *)
%Y Cf. A180045 (numbers (ab+1)(ac+1), a > b > c > 0), A320883 (subsequence of 3-smooth terms), A320884 (subsequence of 5-smooth terms), A002473 (7-smooth numbers).
%K nonn,fini
%O 1,1
%A _Jon E. Schoenfield_, Feb 22 2020