A272331 Refactorable Fibonacci numbers.

1, 2, 8, 46368, 4807526976

Offset: 1

Author

Waldemar Puszkarz, Apr 25 2016

Keywords

• nonn
• fini
• full

Comments

Luca & Young prove that there are no more terms in this sequence. - Charles R Greathouse IV, Apr 27 2016

Examples

			8 is a term as a Fibonacci number that is divisible by the number of its divisors, (1,2,4,8), which is 4.
		

Links

• Florian Luca and Paul Thomas Young, On the number of divisors of n! and of the Fibonacci numbers

Crossrefs

Intersection of A000045 (Fibonacci numbers) and A033950 (refactorable numbers).

Cf. A000005 (number of divisors), A160683.

Programs

Maple

select(t -> t mod numtheory:-tau(t) = 0, map(combinat:-fibonacci, [$2..200])); # Robert Israel, Apr 27 2016

Mathematica

DeleteDuplicates@Select[Fibonacci@Range@200, Divisible[#, IntegerLength@#]&]

PARI

for(n=2, 200, fn=fibonacci(n); fn%numdiv(fn)==0&&print1(fn ", "))

Formula

a(n) = A000045(A160683(n+1)). - Michel Marcus, Apr 25 2016