A075740 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.

1, 55, 377, 17711, 121393, 5702887, 139583862445, 1304969544928657, 5527939700884757, 259695496911122585, 679891637638612258, 12200160415121876738, 19740274219868223167, 31940434634990099905

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..50

Example

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.

Maple

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);

Mathematica

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 *)

Prog

(PARI) {for(n=1, 100, if(moebius(n)==1&&moebius(k=fibonacci(n))==1, print1(k, ", ")))}

Crossrefs

Cf. A000045, A008683, A030229, A084278.

Sequence in context: A020280 A063653 A222348 * A340240 A355511 A129217

Adjacent sequences: A075737 A075738 A075739 * A075741 A075742 A075743

Keyword

easy,nonn

Author

Jani Melik, Oct 07 2002

Extensions

Edited by Klaus Brockhaus, May 25 2003

Added "squarefree" to definition. - N. J. A. Sloane, Jul 31 2020

Status

approved