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A063375 Number of divisors of Fibonacci(n).

%I A063375 #40 Jan 05 2025 19:51:36
%S A063375 1,1,2,2,2,4,2,4,4,4,2,15,2,4,8,8,2,16,4,16,8,4,2,72,6,4,16,16,2,64,4,
%T A063375 16,8,4,8,160,8,8,8,64,4,64,2,32,32,8,2,336,8,48,8,16,4,128,16,96,32,
%U A063375 8,4,960,4,8,32,64,8,64,8,32,32,128,4,1536,4,16,48,32,16,128,4,512,128,8
%N A063375 Number of divisors of Fibonacci(n).
%H A063375 Amiram Eldar, <a href="/A063375/b063375.txt">Table of n, a(n) for n = 1..1408</a> (terms 1..1000 from T. D. Noe using Blair Kelly's data)
%H A063375 Blair Kelly, <a href="http://mersennus.net/fibonacci/">Fibonacci and Lucas Factorizations</a>.
%H A063375 Florian Luca, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/37-3/luca.pdf">Arithmetic Functions of Fibonacci Numbers</a>, The Fibonacci Quarterly, Vol. 37, No. 3 (1999), pp. 265-268.
%F A063375 a(n) = A000005(A000045(n)). - _Omar E. Pol_, Dec 20 2008
%F A063375 a(n) >= A000045(A000005(n)), with equality if and only if n = 1, 2 or 4 (Luca, 1999). - _Amiram Eldar_, Jan 12 2022
%t A063375 Table[Length[Divisors[Fibonacci[n]]], {n, 120}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 01 2011 *)
%t A063375 Table[DivisorSigma[0, Fibonacci[n]], {n, 1, 100}] (* _Vaclav Kotesovec_, Feb 13 2019 *)
%o A063375 (PARI) j=[]; for(n=1,150,j=concat(j,numdiv(fibonacci(n)))); j
%o A063375 (PARI) for (n = 1, 466, write("b063375.txt", n, " ", numdiv(fibonacci(n)))) \\ _Harry J. Smith_, Aug 20 2009
%Y A063375 Cf. A000005, A000045.
%K A063375 nonn
%O A063375 1,3
%A A063375 _Jason Earls_, Jul 23 2001