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%I #11 Jul 09 2018 01:40:52
%S 2,5,3,17,11,7,9,33,67,57,59,39,105,185,191,123,225,219,239,159,319,
%T 283,251,167,335,111,297,175,233,155,103,91,107,71,31,41,27,193,129,
%U 231,171,463,327,411,859,731,487,649,639,1153,1563,1607,1071,1215,1307,871,1161
%N 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.
%F a(n) = Min{k; A087227(k)=n}, where A087227(k) = A001221(A087226(k)); A087226(k) = lcm(terms in Collatz trajectory of k).
%e 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.
%t 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
%Y Cf. A006370, A087226, A086227, A078719, A001221.
%K nonn
%O 1,1
%A _Labos Elemer_, Aug 28 2003
%E Edited by _Jon E. Schoenfield_, Jul 09 2018