I have a question: How can I calculate
$$\sum_{i=1\atop \gcd(i,75)=1}^{75} i=?$$
2026-04-03 23:07:36.1775257656
Calculate the sum under gcd
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See, they come in pairs: if $\gcd(i,75)=1$, then so is $\gcd(75-i,75)$. Obviously, sum of the numbers in each pair is 75; as for the number of pairs, it is half the number of numbers less than 75 and coprime to it, which is given by the totient function.