A306415 Numbers k such that A179682(k) <> A033996(k).
0, 8, 24, 48, 49, 80, 120, 168, 224, 242, 288, 360, 440, 528, 624, 675, 728, 840, 960, 1088, 1224, 1368, 1444, 1520, 1680, 1681, 1848, 2024, 2208, 2400, 2600, 2645, 2808, 3024, 3248, 3480, 3720, 3968, 4224, 4374, 4488, 4760, 5040, 5328, 5624, 5928, 6240, 6560, 6727, 6888, 7224, 7568, 7920, 8280, 8648, 9024, 9408, 9800, 10200, 10608
Offset: 1
Keywords
Examples
24 is a term because A179682(24) = 242: 24 < 242 < 4*24*25 and 24*25*242*243 = 5940^2.
Programs
-
Maple
A179682:= proc(n) local F, t, p, k0, d, k, a, j; p:= max(map(t -> `if`(t[2]::odd, t[1], NULL), [op(ifactors(n)[2]), op(ifactors(n+1)[2])])); if n mod p = 0 then k0:= n+p-1; d:= 1; else k0:= n+1; d:= p-1; fi; t:= n*(n+1)/4; for a from k0 by p do for k in [a, a+d] do if issqr(k*(k+1)*t) then return k fi od od end proc: f(0):= 1: select(t -> A179682(t) <> 4*t*(t+1), [$0..11000]);
Comments