A074691 Squarefree Fibonacci numbers with odd number of prime factors.

2, 3, 5, 13, 89, 233, 610, 987, 1597, 10946, 28657, 514229, 3524578, 9227465, 24157817, 39088169, 63245986, 433494437, 701408733, 1134903170, 1836311903, 2971215073, 7778742049, 20365011074, 365435296162, 591286729879

Offset: 1

Author

Felice Russo, Sep 03 2002

Keywords

• easy
• nice
• nonn

Comments

Agrees for a long time with sequence of Fibonacci numbers whose number of divisors is a Fibonacci number.

Examples

			610 belongs to the sequence because it has 3 prime factors (2, 5, 61); it also has 8 divisors (1, 2, 5, 10, 61, 122, 305, 610).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..575 (terms 1..100 from T. D. Noe)

Crossrefs

Subsequence of A061305 (squarefree Fibonacci numbers).

Cf. A000045.

Cf. A022307, A075735.

Programs

Maple

with(combinat, fibonacci): m2_fib := proc(n); if (numtheory[mobius](fibonacci(n))=-1) then RETURN(fibonacci(n)); fi; end: seq(m2_fib(i), i=1..100);

Mathematica

Select[Fibonacci[Range[80]], MoebiusMu[#] == -1 &] (* Harvey P. Dale, Aug 23 2011 *)

Formula

Fibonacci(n) such that mu(Fibonacci(n)) = -1, where mu(n) is the Moebius mu function (A008683).

Extensions

More terms from Jani Melik, Oct 07 2002