§27.20 Methods of Computation: Other Number-Theoretic Functions
ⓘ
- Keywords:
- computation, number-theoretic functions
- Referenced by:
- §27.20, Erratum (V1.0.11) for Section 27.20
- Permalink:
- http://dlmf.nist.gov/27.20
- Replacement (effective with 1.0.11):
-
27.20 which read,
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
. A similar recursion formula obtained by differentiating
(27.14.18) can be used to calculate Ramanujan’s function
, and the values can be checked by the congruence
(27.14.20).
For further information see Lehmer (1941, pp. 5–83) and
Lehmer (1943, pp. 483–492).
was replaced. - See also:
- Annotations for Ch.27
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).
. See Calkin