A332764 7-smooth numbers of the form (ab+1)*(ac+1), a > b > c > 0.

28, 45, 96, 120, 126, 175, 225, 280, 288, 336, 378, 441, 540, 560, 630, 640, 672, 1080, 1200, 1225, 1470, 1680, 1701, 1792, 1920, 2016, 2160, 2520, 2835, 3136, 3888, 3969, 4000, 4200, 4500, 4608, 5250, 5600, 5760, 6480, 6860, 7200, 7840, 7875, 8400, 8640, 8960

Offset: 1

Author

Jon E. Schoenfield, Feb 22 2020

Keywords

• nonn
• fini

Comments

Sequence is finite (see comments at A320884).

Links

• David A. Corneth, Table of n, a(n) for n = 1..1072

Crossrefs

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).

Programs

Mathematica

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 *)

Formula

Intersection of A002473 and A180045.