A178763 Product of primitive prime factors of Fibonacci(n).

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

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