|
%I #12 Jul 31 2020 11:52:57
%S 1,55,377,17711,121393,5702887,139583862445,1304969544928657,
%T 5527939700884757,259695496911122585,679891637638612258,
%U 12200160415121876738,19740274219868223167,31940434634990099905
%N Squarefree Fibonacci numbers which are the product of an even number of distinct primes and whose index is also squarefree and the product of an even number of distinct primes.
%H Vincenzo Librandi, <a href="/A075740/b075740.txt">Table of n, a(n) for n = 1..50</a>
%e 55 is in the sequence since 55 = fibonacci(10), 55 = 5*11, 10 = 2*5; 377 is in the sequence since 377 = fibonacci(14), 377 = 13*29, 14 = 2*7.
%p with(combinat, fibonacci): m1_supM_fib := proc(n); if (numtheory[mobius](n)=1) then if (numtheory[mobius](fibonacci(n))=1) then RETURN(fibonacci(n)); fi; fi; end: seq(m1_supM_fib(i), i=1..160);
%t pendpQ[n_]:=Module[{f=Transpose[FactorInteger[n]]},EvenQ[Length[ f[[1]]]] && Max[f[[2]]]==1]; Join[{1},Transpose[Select[Table[{n,Fibonacci[n]},{n,150}], pendpQ[#[[1]]] && pendpQ[#[[2]]]&]][[2]]] (* _Harvey P. Dale_, Feb 05 2014 *)
%o (PARI) {for(n=1,100,if(moebius(n)==1&&moebius(k=fibonacci(n))==1,print1(k,",")))}
%Y Cf. A000045, A008683, A030229, A084278.
%K easy,nonn
%O 1,2
%A _Jani Melik_, Oct 07 2002
%E Edited by _Klaus Brockhaus_, May 25 2003
%E Added "squarefree" to definition. - _N. J. A. Sloane_, Jul 31 2020
|
