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

%I A174291 #29 Sep 08 2022 08:45:51
%S A174291 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 A174291 87,88,93,96,97,110,112,115,123,131,137,143,146,149,157,161,163,178,
%U A174291 184,186,187,189,196,197,209,211,214,215,221,223,225,232,239,242,243,246
%N A174291 Numbers n such that bigomega(Fibonacci(n)) is a perfect square.
%C A174291 Places n such that A001222(A000045(n)) is a perfect square.
%D A174291 Majorie Bicknell and Verner E Hoggatt, Fibonacci's Problem Book, Fibonacci Association, San Jose, Calif., 1974.
%H A174291 Amiram Eldar, <a href="/A174291/b174291.txt">Table of n, a(n) for n = 1..236</a>
%H A174291 Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas Factorizations</a>
%F A174291 {n: A038575(n) in A000290}.
%e A174291 bigomega(Fibonacci(1))= 0.
%e A174291 bigomega(Fibonacci(2))= bigomega(Fibonacci(3))=bigomega(Fibonacci(5))=1.
%e A174291 bigomega(Fibonacci(20))= 4, bigomega(Fibonacci(336))= 25.
%e A174291 bigomega(Fibonacci(359))= 1 because Fibonacci(359) is prime.
%p A174291 A174291 := proc(n) if issqr( numtheory[bigomega](combinat[fibonacci](n)) ) then printf("%d,",n) ; fi ; return ; end proc:
%p A174291 seq(A174291(n),n=1..90) ; # _R. J. Mathar_, Jun 01 2011
%t A174291 Select[Range@ 250, IntegerQ@ Sqrt@ PrimeOmega@ Fibonacci@ # &] (* _Michael De Vlieger_, Oct 15 2019 *)
%o A174291 (PARI) isok(n) = issquare(bigomega(fibonacci(n))); \\ _Michel Marcus_, Oct 15 2019
%o A174291 (Magma) [k:k in [1..240]| IsSquare(#PrimeDivisors(Fibonacci(k)))]; // _Marius A. Burtea_, Oct 15 2019
%Y A174291 Cf. A038575, A022307, A000045.
%K A174291 nonn
%O A174291 1,2
%A A174291 _Michel Lagneau_, Mar 15 2010
%E A174291 a(1)=0 removed by _Amiram Eldar_, Oct 15 2019