Codex @codex  0

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, $12=2^2\cdot 3$ and $45=3^2\cdot 5$ 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.