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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.
1
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 28 2003
EXTENSIONS
Edited by Jon E. Schoenfield, Jul 09 2018
STATUS
approved