A174291 - OEIS

%I #29 Sep 08 2022 08:45:51

%S 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,

%T 87,88,93,96,97,110,112,115,123,131,137,143,146,149,157,161,163,178,

%U 184,186,187,189,196,197,209,211,214,215,221,223,225,232,239,242,243,246

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

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

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

%H Amiram Eldar, <a href="/A174291/b174291.txt">Table of n, a(n) for n = 1..236</a>

%H Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas Factorizations</a>

%F {n: A038575(n) in A000290}.

%e bigomega(Fibonacci(1))= 0.

%e bigomega(Fibonacci(2))= bigomega(Fibonacci(3))=bigomega(Fibonacci(5))=1.

%e bigomega(Fibonacci(20))= 4, bigomega(Fibonacci(336))= 25.

%e bigomega(Fibonacci(359))= 1 because Fibonacci(359) is prime.

%p A174291 := proc(n) if issqr( numtheory[bigomega](combinat[fibonacci](n)) ) then printf("%d,",n) ; fi ; return ; end proc:

%p seq(A174291(n),n=1..90) ; # _R. J. Mathar_, Jun 01 2011

%t Select[Range@ 250, IntegerQ@ Sqrt@ PrimeOmega@ Fibonacci@ # &] (* _Michael De Vlieger_, Oct 15 2019 *)

%o (PARI) isok(n) = issquare(bigomega(fibonacci(n))); \\ _Michel Marcus_, Oct 15 2019

%o (Magma) [k:k in [1..240]| IsSquare(#PrimeDivisors(Fibonacci(k)))]; // _Marius A. Burtea_, Oct 15 2019

%Y Cf. A038575, A022307, A000045.

%K nonn

%O 1,2

%A _Michel Lagneau_, Mar 15 2010

%E a(1)=0 removed by _Amiram Eldar_, Oct 15 2019