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A075740
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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.
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2
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1, 55, 377, 17711, 121393, 5702887, 139583862445, 1304969544928657, 5527939700884757, 259695496911122585, 679891637638612258, 12200160415121876738, 19740274219868223167, 31940434634990099905
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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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 *)
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PROG
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(PARI) {for(n=1, 100, if(moebius(n)==1&&moebius(k=fibonacci(n))==1, print1(k, ", ")))}
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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