n∑d∣n∑i=1n/di[gcd(i,n/d)==1]n\sum\limits_{d|n}\sum\limits^{n/d}_{i=1}i[gcd(i,n/d)==1]nd∣n∑i=1∑n/di[gcd(i,n/d)==1] n∑d∣n∑i=1ni[gcd(i,n)==1]n\sum\limits_{d|n}\sum\limits^{n}_{i=1}i[gcd(i,n)==1]nd∣n∑i=1∑ni[gcd(i,n)==1]
