The sum of all the elements in the set n1,2,,100 : (n,2040)=1 is equal to ________.

Question

The sum of all the elements in the set $\{n\in\{1,2,\ldots,100\} : \gcd(n,2040)=1\}$ is equal to \_\_\_\_\_\_\_\_.

Answer: 1251

Accepted Answer

$2040 = 2^3\times3\times5\times17$. Numbers in $\{1,\ldots,100\}$ coprime to $2040$ must avoid all factors of $2,3,5,17$:
$$\{1,7,11,13,19,23,29,31,37,41,43,47,53,59,61,67,71,73,77,79,83,89,91,97\}.$$

Their sum is $1251$.

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