A065451 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

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.

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

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

CROSSREFS

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

Sequence in context: A366873 A345656 A308742 * A178148 A337681 A245180

Adjacent sequences: A065448 A065449 A065450 * A065452 A065453 A065454

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Nov 18 2001

EXTENSIONS

More terms from several correspondents, Nov 19 2001

STATUS

approved