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

1,2

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000010, A000045, A134492, A280681.

Sequence in context: A049911 A056712 A204540 * A330990 A337129 A002087

Adjacent sequences: A280589 A280590 A280591 * A280593 A280594 A280595

Keyword

nonn,look

Author

Altug Alkan, Jan 06 2017

Status

approved