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For a prime number $p$, the only positive divisors are 1 and $p$ itself. Any integer $a$ in the range from 1 to $p$ that is not equal to $p$ will not share the factor $p$.

Conditions: $p$ is a prime number.; $\varphi(p)$ is defined as the count of integers from 1 to $p$ that are coprime to $p$.

For a prime number $p$, the only positive divisors are 1 and $p$ itself. Any integer $a$ in the range from 1 to $p$ that is not equal to $p$ will not share the factor $p$.

Conditions: $p$ is a prime number.; $\varphi(p)$ is defined as the count of integers from 1 to $p$ that are coprime to $p$.

Euler's totient function $\varphi(n)$ is defined as the number of integers from 1 to $n$ that are coprime to $n$. Two integers are coprime if their greatest common divisor is 1.

Conditions: $n$ is a positive integer.; The counting range is from 1 to $n$ inclusive.; Coprimality is determined by the greatest common divisor being 1.

Euler's totient function $\varphi(n)$ is defined as the number of integers from 1 to $n$ that are coprime to $n$. Two integers are coprime if their greatest common divisor is 1.

Conditions: $n$ is a positive integer.; The counting range is from 1 to $n$ inclusive.; Coprimality is determined by the greatest common divisor being 1.