`primeFactors`

computes a vector containing the prime factors of
`n`

. `radical`

returns the product of those unique prime
factors.

1 2 | ```
primeFactors(n)
radical(n)
``` |

`n` |
nonnegative integer |

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)

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)
``` |

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