A075742 Fibonacci numbers for which both the value and index are the product of an odd number of distinct primes; that is, numbers Fibonacci(k) for which mu(k) = mu(Fibonacci(k)) = -1.

2, 5, 13, 89, 233, 1597, 28657, 514229, 24157817, 433494437, 2971215073, 44945570212853, 190392490709135, 99194853094755497, 1500520536206896083277, 3928413764606871165730, 1066340417491710595814572169, 19134702400093278081449423917

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Example

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, ...

Maple

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:

Crossrefs

Cf. A000045, A008683, A030059, A074691.

Sequence in context: A325627 A075736 A030426 * A075737 A100843 A082101

Adjacent sequences: A075739 A075740 A075741 * A075743 A075744 A075745

Keyword

easy,nonn,changed

Author

Jani Melik, Oct 07 2002

Extensions

Incorrect 83621143489848422977 removed and more terms from Sean A. Irvine, Mar 05 2025

Status

approved