No subject

[Ctibor.ZIZKA]

No, n*p(n) / (n+p(n)) is never an integer.
Moreover, it is always an irreducible fraction.

Notice that p(n) > n and thus gcd(p(n),n)=1, implying that
gcd(p(n)+n,n)=1 and gcd(p(n),n+p(n))=1.
Therefore,
gcd(n+p(n),n*p(n)) = 1, implying that
the numerator and denominator of n*p(n) / (n+p(n)) have no common
non-trivial factors.

Regards,
Max

On Tue, Mar 4, 2008 at 12:15 AM, Ctibor.ZIZKA <Ctibor.ZIZKA at seznam.cz> wrote:
> Re A033286,A016688
>  Does an n exist :
>
>  n*p(n) / (n+p(n)) is an integer ?
>
>  p(n) is  n-th prime
>
>  Ctibor O. Zizka
>