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Smallest Fibonacci number with n distinct prime factors.
14

%I #20 Oct 15 2019 07:51:04

%S 1,2,21,610,6765,832040,102334155,190392490709135,1548008755920,

%T 23416728348467685,2880067194370816120,81055900096023504197206408605,

%U 2706074082469569338358691163510069157,5358359254990966640871840,57602132235424755886206198685365216,18547707689471986212190138521399707760

%N Smallest Fibonacci number with n distinct prime factors.

%H Amiram Eldar, <a href="/A060319/b060319.txt">Table of n, a(n) for n = 0..40</a>

%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html">Fibonacci numbers with tables of F(0)-F(500)</a>

%e a(5) = F(30) = 832040 = 2^3 * 5 * 11 * 41 * 61.

%t f[n_]:=Length@FactorInteger[Fibonacci[n]]; lst={};Do[Do[If[f[n]==q,Print[Fibonacci[n]];AppendTo[lst,Fibonacci[n]];Break[]],{n,280}],{q,18}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 23 2009 *)

%t First /@ SortBy[#, Last] &@ Map[#[[1]] &, Values@ GroupBy[#, Last]] &@ Table[{#, PrimeNu@ #} &@ Fibonacci@ n, {n, 2, 200}] (* _Michael De Vlieger_, Feb 18 2017, Version 10 *)

%Y Cf. A001605, A005478, A060320.

%Y Row n=1 of A303218.

%K nonn

%O 0,2

%A _Labos Elemer_, Mar 28 2001