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A174291 Numbers n such that bigomega(Fibonacci(n)) is a perfect square. 1
1, 2, 3, 4, 5, 7, 11, 13, 17, 20, 23, 24, 27, 28, 29, 32, 43, 47, 52, 55, 74, 77, 80, 83, 85, 87, 88, 93, 96, 97, 110, 112, 115, 123, 131, 137, 143, 146, 149, 157, 161, 163, 178, 184, 186, 187, 189, 196, 197, 209, 211, 214, 215, 221, 223, 225, 232, 239, 242, 243, 246 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Places n such that A001222(A000045(n)) is a perfect square.

REFERENCES

Majorie Bicknell and Verner E Hoggatt, Fibonacci's Problem Book, Fibonacci Association, San Jose, Calif., 1974.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..236

Blair Kelly, Fibonacci and Lucas Factorizations

FORMULA

{n: A038575(n) in A000290}.

EXAMPLE

bigomega(Fibonacci(1))= 0.

bigomega(Fibonacci(2))= bigomega(Fibonacci(3))=bigomega(Fibonacci(5))=1.

bigomega(Fibonacci(20))= 4, bigomega(Fibonacci(336))= 25.

bigomega(Fibonacci(359))= 1 because Fibonacci(359) is prime.

MAPLE

A174291 := proc(n) if issqr( numtheory[bigomega](combinat[fibonacci](n)) ) then printf("%d, ", n) ; fi ; return ; end proc:

seq(A174291(n), n=1..90) ; # R. J. Mathar, Jun 01 2011

MATHEMATICA

Select[Range@ 250, IntegerQ@ Sqrt@ PrimeOmega@ Fibonacci@ # &] (* Michael De Vlieger, Oct 15 2019 *)

PROG

(PARI) isok(n) = issquare(bigomega(fibonacci(n))); \\ Michel Marcus, Oct 15 2019

(MAGMA) [k:k in [1..240]| IsSquare(#PrimeDivisors(Fibonacci(k)))]; // Marius A. Burtea, Oct 15 2019

CROSSREFS

Cf. A038575, A022307, A000045.

Sequence in context: A046022 A175787 A073019 * A007885 A192586 A003037

Adjacent sequences:  A174288 A174289 A174290 * A174292 A174293 A174294

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 15 2010

EXTENSIONS

a(1)=0 removed by Amiram Eldar, Oct 15 2019

STATUS

approved

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Last modified January 17 09:50 EST 2020. Contains 330949 sequences. (Running on oeis4.)