# Name for summation that returns GCD(k,n)

Define

$$H(k,n)=2\sum_{i=1}^{n-1}\left\lfloor\frac{ki}{n}\right\rfloor\;.$$

We can prove that $H(k,n)=nk-k-n+\gcd(k,n)$. Does this $H$ carry some known name?

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