A280592 Numbers n such that phi(n) is a Fibonacci number.

1, 2, 3, 4, 6, 15, 16, 20, 24, 30, 185, 219, 273, 285, 292, 296, 304, 315, 364, 370, 380, 432, 438, 444, 456, 468, 504, 540, 546, 570, 630, 3235, 5176, 6470, 7764, 46843, 47423, 47693, 48053, 50431, 52403, 56231, 57965, 59555, 62855, 67655, 67865, 70735, 72123, 72297, 73473

Offset: 1

Author

Altug Alkan, Jan 06 2017

Keywords

• nonn
• look

Comments

Note that the sequence of corresponding Fibonacci numbers is not the same as A134492. See also A280681.

Examples

			24 is a term because phi(24) = 8 is a Fibonacci number.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2075

Crossrefs

Cf. A000010, A000045, A134492, A280681.

Programs

Maple

fibs:= {seq(combinat:-fibonacci(n),n=1..30)}:
N:= combinat:-fibonacci(31):
sort(convert(select(t -> t <= N, map(t -> op(numtheory:-invphi(t)), fibs)), list)); # Robert Israel, Nov 20 2019

Mathematica

Module[{fibs=Fibonacci[Range[30]]},Select[Range[80000],MemberQ[ fibs,EulerPhi[ #]]&]] (* Harvey P. Dale, Jul 04 2021 *)

PARI

isFibonacci(n)=my(k=n^2); issquare(k+=(k+1)<<2) || (n>0 && issquare(k-8));
is(n)=isFibonacci(eulerphi(n));