Functions primes() and factorize() cut-and-pasted from
Bill Venebles's conf.design package, version 0.0-3. Function
primes(n) returns a vector of all primes not exceeding
n; function factorize(n) returns an integer vector of
nondecreasing primes whose product is n. The others are multiplicative functions, defined in Hardy and
Wright:
Function divisor(), also written
$\sigma_k(n)$, is the divisor function defined on
p239. This gives the sum of the $k^{\rm th}$ powers of all
the divisors of n. Setting $k=0$ corresponds to
$d(n)$, which gives the number of divisors of n.
mobius() is the M"{o}bius function (p234), giving zero if
n has a repeated prime factor, and $(-1)^q$ where
$n=p_1p_2\ldots p_q$ otherwise.
totient() is Euler's totient function (p52), giving the number
of integers smaller than n and relatively prime to it.