# factorize: Prime Factors In numbers: Number-Theoretic Functions

## Description

`primeFactors` computes a vector containing the prime factors of `n`. `radical` returns the product of those unique prime factors.

## Usage

 ```1 2``` ``` 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

## Value

Vector containing the prime factors of `n`, resp. the product of unique prime factors.

`divisors`, `gmp::factorize`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ``` 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) ```