

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
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OFFSET

1,2


COMMENTS



REFERENCES

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


LINKS



FORMULA



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:


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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



