A087228 a(n) is the smallest number k such that the LCM of the terms of the Collatz trajectory of k has n distinct prime factors.
2, 5, 3, 17, 11, 7, 9, 33, 67, 57, 59, 39, 105, 185, 191, 123, 225, 219, 239, 159, 319, 283, 251, 167, 335, 111, 297, 175, 233, 155, 103, 91, 107, 71, 31, 41, 27, 193, 129, 231, 171, 463, 327, 411, 859, 731, 487, 649, 639, 1153, 1563, 1607, 1071, 1215, 1307, 871, 1161
Offset: 1
Keywords
Examples
a(10)=57 because 57 is the smallest number such that the LCM of the terms in its Collatz trajectory has 10 different prime factors: A082226(57) = 864203580240 = 2^4*3*5*7*11*13*17*19*37*43.
Programs
-
Mathematica
c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1)c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] ef[x_] := Length[FactorInteger[Apply[LCM, fpl[x]]]] t=Table[0, {256}]; Do[s=ef[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 1000}]; t
Formula
Extensions
Edited by Jon E. Schoenfield, Jul 09 2018