%I #5 Oct 02 2013 15:12:51
%S 12,24,25,36,48,50,56,60,72,75,84,91,96,100,108,110,112,120,132,144,
%T 150,153,156,168,175,180,182,192,200,204,216,220,224,225,228,240,252,
%U 264,273,275,276,280,300,306,312,324,325,330,336,342,348,350,360,364,372
%N Numbers n such that the number of divisors of Fibonacci(n), tau(Fibonacci(n)), is not a perfect power of 2.
%C Has many terms in common with A023172 (41 below 1000), but neither is a subsequence of the other since 125 is not in this sequence.
%H Blair Kelly, <a href="http://mersennus.net/fibonacci/">Fibonacci and Lucas Factorizations</a>.
%F a(n) = {k: tau(Fibonacci(k)) != 2^i for all i}.
%e F(12) = 144 has 15 divisors: {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144}. Since 15 is not a power of 2, 12 is in the sequence.
%e F(24) = 46368 has 72 divisors. Since 72 is not a power of 2, 24 is in the sequence.
%t Do[If[ !IntegerQ[Log[2, DivisorSigma[0, Fibonacci[n]]]], Print[n]], {n, 10^3}]
%K nonn
%O 1,1
%A _Ryan Propper_, Jun 01 2006
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