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%I #12 Jul 08 2019 04:05:07
%S 1,1,2,3,5,1,13,7,17,11,89,1,233,29,61,47,1597,19,4181,41,421,199,
%T 28657,23,3001,521,5777,281,514229,31,1346269,2207,19801,3571,141961,
%U 107,24157817,9349,135721,2161,165580141,211,433494437,13201,109441,64079
%N Product of primitive prime factors of Fibonacci(n).
%C Same as A001578 for the first 18 terms.
%C Let b(n) be the greatest divisor of Fibonacci(n) that is coprime to Fibonacci(m) for all positive integers m < n, then a(n) = b(n) for all n, provided that no Wall-Sun-Sun prime exists. Otherwise, if p is a Wall-Sun-Sun prime and A001177(p) = k (then A001177(p^2) = k), then p^2 divides b(k), but by definition a(k) is squarefree. - _Jianing Song_, Jul 02 2019
%H T. D. Noe, <a href="/A178763/b178763.txt">Table of n, a(n) for n = 1..1000</a>
%H Dov Jarden, <a href="/A001602/a001602.pdf">Recurring Sequences</a>, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See pp. 60-64 for a table of the first 385 terms.
%H Florian Luca, Carl Pomerance, and Stephen Wagner, <a href="http://www.math.dartmouth.edu/~carlp/fibinttalk.pdf">Fibonacci Integers (preprint)</a>
%F a(n) = A061446(n) / A178764(n).
%F a(n) = A061446(n) / gcd(A061446(n), n) if n != 5, 6, provided that no Wall-Sun-Sun prime exists. - _Jianing Song_, Jul 02 2019
%o (PARI) a(n)=my(d=divisors(n), f=fibonacci(n), t); t=lcm(apply(fibonacci,d[1..#d-1])); while((t=gcd(t,f))>1, f/=t); f \\ _Charles R Greathouse IV_, Nov 30 2016
%Y Cf. A061446, A086597, A152012 (Indices of prime terms).
%K nonn
%O 1,3
%A _T. D. Noe_, Jun 10 2010
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