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Indices of Fibonacci numbers with 11 distinct prime factors.
3

%I #17 May 05 2024 19:19:16

%S 140,144,150,160,162,190,204,208,230,234,261,285,306,310,345,351,354,

%T 372,387,388,399,438,459,469,470,475,483,485,488,507,508,518,531,549,

%U 568,596,598,632,656,671,686,688,715,788,806,808,822,834,844,872,873,874,902,925,1005,1048,1052,1058,1073,1076,1083,1101,1113,1124,1131,1146,1158,1162,1166,1173,1195,1205,1221

%N Indices of Fibonacci numbers with 11 distinct prime factors.

%H Amiram Eldar, <a href="/A114825/b114825.txt">Table of n, a(n) for n = 1..81</a>

%H Blair Kelly, <a href="http://mersennus.net/fibonacci/">Fibonacci and Lucas Factorizations</a>.

%e a(1)=140 because the 140th Fibonacci number (i.e., 81055900096023504197206408605) consists of 11 distinct prime factors (i.e., 3 * 5 * 11 * 13 * 29 * 41 * 71 * 281 * 911 * 141961 * 12317523121).

%o (PARI) n=1;while(n<315,if(omega(fibonacci(n))==11,print1(n,", "));n++)

%Y Column k=11 of A303217.

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Feb 19 2006

%E More terms from _Ryan Propper_, Apr 26 2006

%E a(52)-a(73) from _Max Alekseyev_, Aug 18 2013