As Pieter Moree
pointed out, I made an error.
For one thing at least,
|1/j(k) - 1/k| is NOT
necessarily <= |2/n -1/(n-1)| < 1/n (or <= 1/k either)!
(I do not know *what* I was thinking)
But the result of
sum{k=1 to n} GCD(k,n) =
n *sum{k|n} phi(k) /k
seems to be right, at least.
:/
Sorry + thanks,
Leroy Quet