primeFactors {numbers} | R Documentation |
Prime Factors
Description
primeFactors
computes a vector containing the prime factors of
n
. radical
returns the product of those unique prime
factors.
Usage
primeFactors(n)
radical(n)
Arguments
n |
nonnegative integer |
Details
Computes the prime factors of n
in ascending order,
each one as often as its multiplicity requires, such that
n == prod(primeFactors(n))
.
## radical() is used in the abc-conjecture:
# abc-triple: 1 <= a < b, a, b coprime, c = a + b
# for every e > 0 there are only finitely many abc-triples with
# c > radical(a*b*c)^(1+e)
Value
Vector containing the prime factors of n
, resp.
the product of unique prime factors.
See Also
divisors
, gmp::factorize
Examples
primeFactors(1002001) # 7 7 11 11 13 13
primeFactors(65537) # is prime
# Euler's calculation
primeFactors(2^32 + 1) # 641 6700417
radical(1002001) # 1001
## Not run:
for (i in 1:99) {
for (j in (i+1):100) {
if (coprime(i, j)) {
k = i + j
r = radical(i*j*k)
q = log(k) / log(r) # 'quality' of the triple
if (q > 1)
cat(q, ":\t", i, ",", j, ",", k, "\n")
}
}
}
## End(Not run)
[Package numbers version 0.8-5 Index]