A084278 Squarefree numbers n which are the product of an even number of distinct primes such that Fibonacci(n) is also squarefree and the product of an even number of distinct primes.

1, 10, 14, 22, 26, 34, 55, 74, 77, 85, 87, 93, 94, 95, 115, 123, 129, 133, 143, 146, 155, 159, 161, 177, 178, 187, 194, 205, 206, 209, 214, 215, 217, 219, 221, 237, 249, 262, 265, 278, 287, 309, 314, 321, 323, 327, 334, 339, 341, 346, 355, 358, 362, 391

Offset

1,2

Comments

The Pocklington-Lehmer "P-1"primality test, as implemented in PARI 2.1.3, was used separately for factors > 10^8 encountered in the computation.

Links

Table of n, a(n) for n=1..54.

Example

34 is in the sequence since Fibonacci(34) = 5702887, 34 = 2*17, 5702887 = 1597*3571; 55 is in the sequence since Fibonacci(55) = 139583862445, 55 = 5*11, 139583862445 = 5*89*661*474541.

Mathematica

endpQ[n_]:=Module[{exp=FactorInteger[n][[All, 2]]}, EvenQ[ Length[ exp]] &&Max[exp]==1]; Join[{1}, Select[Range[400], AllTrue[{ #, Fibonacci[ #]}, endpQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 31 2020 *)

Prog

(PARI) {for(n=1, 391, if(moebius(n)==1&&moebius(fibonacci(n))==1, print1(n, ", ")))}

Crossrefs

Cf. A000045, A008683, A030229, A075740.

Sequence in context: A151740 A136802 A362866 * A286843 A069207 A168671

Adjacent sequences: A084275 A084276 A084277 * A084279 A084280 A084281

Keyword

easy,nonn

Author

Klaus Brockhaus, May 25 2003

Extensions

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

Status

approved