To calculate a multiplicative function it suffices to determine its values at the prime powers and then use (27.3.2). For a completely multiplicative function we use the values at the primes together with (27.3.10).

The recursion formulas (27.14.6) and (27.14.7) can be used to calculate the partition function $p\left(n\right)$ for $$. See Calkin et al. (2007), and Lehmer (1941, pp. 5–83). To compute a particular value $p\left(n\right)$ it is better to use the Hardy-Ramanujan-Radematcher series (27.14.9). See Johansson (2012).