A065451 a(n) = Fibonacci(phi(n)), a(0) = 0.

0, 1, 1, 1, 1, 3, 1, 8, 3, 8, 3, 55, 3, 144, 8, 21, 21, 987, 8, 2584, 21, 144, 55, 17711, 21, 6765, 144, 2584, 144, 317811, 21, 832040, 987, 6765, 987, 46368, 144, 14930352, 2584, 46368, 987, 102334155, 144, 267914296, 6765, 46368, 17711, 1836311903

Offset: 0

Author

Joseph L. Pe, Nov 18 2001

Keywords

• nonn

Examples

			a(13) = F(phi(13)) = F(12) = 144.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Florian Luca, Arithmetic Functions of Fibonacci Numbers, The Fibonacci Quarterly, Vol. 37, No. 3 (1999), pp. 265-268.
• Joseph L. Pe, The Euler Phibonacci Sequence: A Problem Proposal with Software, 2001.

Crossrefs

Cf. A000010, A000045, A065449 (phi(Fibonacci(n))).

Programs

Magma

[0] cat [Fibonacci(EulerPhi(n)): n in [1..50]]; // G. C. Greubel, Jan 18 2018

Mathematica

Table[ Fibonacci[ EulerPhi[ n]], {n, 0, 60} ]

PARI

for(n=1,75,print1(fibonacci(eulerphi(n)),","))

PARI

{ for (n=0, 1000, if (n, a=fibonacci(eulerphi(n)), a=0); write("b065451.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 20 2009

Formula

a(n) = A000045(A000010(n)).

a(n) <= A065449(n), with equality if and only if n = 1, 2 or 3 (Luca, 1999). - Amiram Eldar, Jan 12 2022

Extensions

More terms from several correspondents, Nov 19 2001