 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, $12=2^2\cdot 3$ 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.

In mathematics, a prime signature typically refers to a specific way of representing numbers or elements related to prime numbers, but the term can also refer to concepts in different mathematical contexts. However, it is most commonly associated with number theory or algebra. One common use of the term "signature" in mathematics relates to the decomposition of integers: 1. **Integer Factorization**: In number theory, the prime signature of an integer can describe its prime factorization.