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

1,1

Comments

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

Links

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

Formula

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

Example

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).

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 *)

Crossrefs

Subsequence of A061305 (squarefree Fibonacci numbers).

Cf. A000045.

Cf. A022307, A075735.

Sequence in context: A265785 A326372 A001685 * A139589 A152114 A139095

Adjacent sequences: A074688 A074689 A074690 * A074692 A074693 A074694

Keyword

easy,nice,nonn

Author

Felice Russo, Sep 03 2002

Extensions

More terms from Jani Melik, Oct 07 2002

Status

approved