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

1,1

Links

Table of n, a(n) for n=1..57.

Formula

a(n) = Min{k; A087227(k)=n}, where A087227(k) = A001221(A087226(k)); A087226(k) = lcm(terms in Collatz trajectory of k).

Example

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.

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

Crossrefs

Cf. A006370, A087226, A086227, A078719, A001221.

Sequence in context: A063703 A109619 A248576 * A285743 A077216 A227617

Adjacent sequences: A087225 A087226 A087227 * A087229 A087230 A087231

Keyword

nonn

Author

Labos Elemer, Aug 28 2003

Extensions

Edited by Jon E. Schoenfield, Jul 09 2018

Status

approved