Notation for power of prime in prime factorization

Question

What's the accepted shorthand for the power of a prime in the prime factorization of a natural number?

For example, $35 000 = 2^3 5^4 7$, so what would the notation be for $f_5(35 000) = 4, f_2(35 000) = 3$, $f_7(35 000) = 1$?

Answer 1

The exponent of $p$ in the prime factorization of $n$ is sometimes called the $p$-adic order or $p$-adic additive valuation and denoted $\nu_p(n)$, but I don't think this notation is universal.