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A178763 Product of primitive prime factors of Fibonacci(n). 6
1, 1, 2, 3, 5, 1, 13, 7, 17, 11, 89, 1, 233, 29, 61, 47, 1597, 19, 4181, 41, 421, 199, 28657, 23, 3001, 521, 5777, 281, 514229, 31, 1346269, 2207, 19801, 3571, 141961, 107, 24157817, 9349, 135721, 2161, 165580141, 211, 433494437, 13201, 109441, 64079 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Same as A001578 for the first 18 terms.

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See pp. 60-64 for a table of the first 385 terms.

Florian Luca, Carl Pomerance, and Stephen Wagner, Fibonacci Integers (preprint)

FORMULA

a(n) = A061446(n) / A178764(n).

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

PROG

(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

CROSSREFS

Cf. A061446, A086597, A152012 (Indices of prime terms).

Sequence in context: A030790 A001578 A262341 * A111141 A069111 A171035

Adjacent sequences:  A178760 A178761 A178762 * A178764 A178765 A178766

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 10 2010

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)