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A075742 Fibonacci numbers, which are the product of an odd number of distinct primes for numbers with the same property (mu(n)=mu(fibonacci(n))=-1). 0

%I #6 Jan 01 2024 13:44:07

%S 2,5,13,89,233,1597,28657,514229,24157817,433494437,2971215073,

%T 44945570212853,190392490709135,99194853094755497,

%U 83621143489848422977,1500520536206896083277,3928413764606871165730

%N Fibonacci numbers, which are the product of an odd number of distinct primes for numbers with the same property (mu(n)=mu(fibonacci(n))=-1).

%e 11 is a prime and fibonacci(11)=89 is a prime, 13 is a prime and fibonacci(13)=233 is a prime, but fibonacci(16)=987=3*7*47 and 16 is not squarefree and 30=2*3*5 is the product of an odd number of distinct primes but fibonacci(30)=832040=2^3*5*11*31*61 is not squarefree, ...

%p with(combinat, fibonacci): m2_supM_fib := proc(n); if (numtheory[mobius](n)=-1) then if (numtheory[mobius](fibonacci(n))=-1) then RETURN(fibonacci(n)); fi; fi; end:

%Y Cf. A000045, A030059, A074691.

%K easy,nonn

%O 1,1

%A _Jani Melik_, Oct 07 2002

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Last modified August 11 11:30 EDT 2024. Contains 375068 sequences. (Running on oeis4.)