Hello

Let gcdsum[n] = gcd(1,1)+gcd(1,2)+gcd(1,3)+ ... +gcd(n,n)
Also gcdsum[n] can be evaluated using :

gcdsum[n] = n*sum(eulerphi(d)/d)  for all d | n

Now to compute all gcdsum values upto n we first need to precompute
all eulerphi and then use a sieve like algorithm to make a table of
all gcdsum .

But can any one tell me a way to compute the gcd sum values without
computing phi . Since a table of eulerphi could be made without
computing prime numbers, but i am unable to extend this idea.

Can any one help ?

Thanks !

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