Modified Euler Phi Function / Sum Of Divisor-Functions Identity

From: Leroy Quet (qqquet_at_mindspring.com)
Date: 10/02/04 

Date: 2 Oct 2004 06:39:58 -0700

Let phi(x,k) = the number of positive integers which are coprime to k
and are <= x.
(So, the standard Euler phi function, phi(k), is phi(k,k).)

Let sigma_q(k) =
sum{j|k} j^q.

If m = positive integer, then:

sum{k=1 to m} sigma_q(k)

=

sum{k|m} sum{j=1 to k} j^q *phi(k/j,k)

(Unless I made an errror..)

(Result is no big deal, but somewhat interesting.)

thanks,
Leroy Quet

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