A111079 - OEIS

A111079

a(n) = gcd(F(n), product{k|n,k<n} F(k)), where F(k) is k-th Fibonacci number.

1, 1, 1, 1, 1, 2, 1, 3, 2, 5, 1, 48, 1, 13, 10, 21, 1, 136, 1, 165, 26, 89, 1, 2016, 5, 233, 34, 1131, 1, 26840, 1, 987, 178, 1597, 65, 139536, 1, 4181, 466, 47355, 1, 1269736, 1, 53133, 10370, 28657, 1, 4358592, 13, 825275, 3194, 364179, 1, 14927768, 445

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

The proper divisors of 16 are 1, 2, 4, 8. So a(16) = gcd(F(16), F(1)*F(2)*F(4)*F(8)) = gcd(987, 1*1*3*21) = 21.

MAPLE

with(combinat): with(numtheory): a:=proc(n) local div: div:=divisors(n): gcd(fibonacci(n), product(fibonacci(div[j]), j=1..tau(n)-1)): end: seq(a(n), n=1..65); # Emeric Deutsch, Oct 12 2005

MATHEMATICA

f[n_] := GCD[Fibonacci[n], Times @@ Fibonacci /@ Most[Divisors[n]]]; Table[ f[n], {n, 55}] (* Robert G. Wilson v, Oct 12 2005 *)

CROSSREFS

Cf. A000045.

Sequence in context: A105800 A365859 A105602 * A165006 A134735 A240867

Adjacent sequences: A111076 A111077 A111078 * A111080 A111081 A111082

KEYWORD

nonn

AUTHOR

Leroy Quet, Oct 11 2005

EXTENSIONS

More terms from Robert G. Wilson v and Emeric Deutsch, Oct 12 2005

STATUS

approved