A081979 Smallest Fibonacci number with 2n divisors, or 0 if no such number exists.

2, 8, 75025, 610

Offset: 1

Author

Amarnath Murthy, Apr 03 2003

Keywords

• nonn
• more

Comments

Further known terms are a(12)=A000045(91); a(16)=A000045(44); a(24)=A000045(50); a(32)=A000045(30); a(36)=A000045(24); a(48)=A000045(56); a(64)=A000045(54); a(80)=A000045(36); a(96)=A000045(182); a(128)=A000045(128); a(168)=A000045(48); a(192)=A000045(110); a(256)=A000045(80), ..., a(688128)=A000045(240) from the Kelly factorizations. - R. J. Mathar, Apr 05 2007

For n prime, a(n) = q*p^(n-1) or p^(2n-1) for some primes p and q since those are the only numbers with 2*n divisors. a(8) = 2584. - Chai Wah Wu, Dec 08 2014

The sequence is restricted to even numbers of divisors since 1 and 144 are the only Fibonacci numbers with an odd number of divisors (because they are the only positive Fibonacci numbers that are squares, see A227875). - Amiram Eldar, Jul 02 2023

Examples

			a(2) = 8 because 8 is the smallest Fibonacci number with 4 divisors (1,2,4,8).
		

Links

• Blair Kelly, Fibonacci Factorizations.

Crossrefs

Cf. A000045, A081978, A227875.

Extensions

Corrected by Emeric Deutsch, Apr 19 2005