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
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
Programs
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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));
Comments