Prime signature
= Prime signature
The prime signature of $n=\prod_{i=1}^r p_i^{a_i}$ is the <multiset> of positive <prime exponents> $a_i$, conventionally sorted. For example, $12=2^2\cdot3$ and $45=3^2\cdot5$ both have signature $(2,1)$. Quantities such as the <divisor function> and the number of <ordered factorizations> depend on this signature rather than the particular <primes>.