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

1,2

Comments

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

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

Formula

{n: A038575(n) in A000290}.

Example

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.

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 *)

Prog

(PARI) isok(n) = issquare(bigomega(fibonacci(n))); \\ Michel Marcus, Oct 15 2019
(Magma) [k:k in [1..240]| IsSquare(#PrimeDivisors(Fibonacci(k)))]; // Marius A. Burtea, Oct 15 2019

Crossrefs

Cf. A038575, A022307, A000045.

Sequence in context: A175787 A345899 A073019 * A007885 A192586 A003037

Adjacent sequences: A174288 A174289 A174290 * A174292 A174293 A174294

Keyword

nonn

Author

Michel Lagneau, Mar 15 2010

Extensions

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

Status

approved