

A275774


Numbers m with the property that, when a and b are positive integers such that a*b = m, ab is a Fibonacci number.


0




OFFSET

1,2


COMMENTS

a(n) is of the form Fibonacci(k) + 1. Is this sequence finite?
There are probably no more terms. If a(9) exists, it is greater than 10^200.  Charles R Greathouse IV, Aug 08 2016


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

35 is in the sequence because A038548(35) = 2 => two decompositions of 35 = 1*35 = 5*7 => 351 = 34 and 72 = 5 are Fibonacci numbers.


MATHEMATICA

Do[ds=Divisors[n]; If[EvenQ[Length[ds]], ok=True; k=1; While[k<=Length[ds]/2&&(ok=IntegerQ[Sqrt[5*(ds[[k]]ds[[k]])^2+4]]IntegerQ[Sqrt[5*(ds[[k]]ds[[k]])^24]]), k++]; If[ok, Print[n]]], {n, 2, 10^7}]


PROG

(PARI) isFibonacci(n)=my(k=n^2); k+=((k+1)<<2); issquare(k)(n>0&&issquare(k8))
is(n)=fordiv(n, d, if(!isFibonacci(abs(n/dd)), return(0))); 1 \\ Charles R Greathouse IV, Aug 08 2016


CROSSREFS

Cf. A000045, A038548.
Sequence in context: A093467 A246640 A080408 * A319323 A341630 A001420
Adjacent sequences: A275771 A275772 A275773 * A275775 A275776 A275777


KEYWORD

nonn


AUTHOR

Michel Lagneau, Aug 08 2016


EXTENSIONS

a(1) inserted by Charles R Greathouse IV, Aug 08 2016


STATUS

approved



