A174291 Numbers n such that bigomega(Fibonacci(n)) is a perfect square.

1, 2, 3, 4, 5, 7, 11, 13, 17, 20, 23, 24, 27, 28, 29, 32, 43, 47, 52, 55, 74, 77, 80, 83, 85, 87, 88, 93, 96, 97, 110, 112, 115, 123, 131, 137, 143, 146, 149, 157, 161, 163, 178, 184, 186, 187, 189, 196, 197, 209, 211, 214, 215, 221, 223, 225, 232, 239, 242, 243, 246

Offset: 1

Author

Michel Lagneau, Mar 15 2010

Keywords

• nonn

Comments

Places n such that A001222(A000045(n)) is a perfect square.

Examples

			bigomega(Fibonacci(1))= 0.
bigomega(Fibonacci(2))= bigomega(Fibonacci(3))=bigomega(Fibonacci(5))=1.
bigomega(Fibonacci(20))= 4, bigomega(Fibonacci(336))= 25.
bigomega(Fibonacci(359))= 1 because Fibonacci(359) is prime.
		

References

• Majorie Bicknell and Verner E Hoggatt, Fibonacci's Problem Book, Fibonacci Association, San Jose, Calif., 1974.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..236
• Blair Kelly, Fibonacci and Lucas Factorizations

Crossrefs

Cf. A038575, A022307, A000045.

Programs

Magma

[k:k in [1..240]| IsSquare(#PrimeDivisors(Fibonacci(k)))]; // Marius A. Burtea, Oct 15 2019

Maple

A174291 := proc(n) if issqr( numtheory[bigomega](combinat[fibonacci](n)) ) then printf("%d,",n) ; fi ; return ; end proc:
seq(A174291(n),n=1..90) ; # R. J. Mathar, Jun 01 2011

Mathematica

Select[Range@ 250, IntegerQ@ Sqrt@ PrimeOmega@ Fibonacci@ # &] (* Michael De Vlieger, Oct 15 2019 *)

PARI

isok(n) = issquare(bigomega(fibonacci(n))); \\ Michel Marcus, Oct 15 2019

Formula

{n: A038575(n) in A000290}.

Extensions

a(1)=0 removed by Amiram Eldar, Oct 15 2019