func E12() (ans int) {
limit := 500
primes := utils.Primes(3)
for i := 1; ; i++ {
if primes[len(primes)-1] <= i+1 {
primes = utils.Primes(2 * (i + 1))
}
n, d := i*(i+1)/2, 1
for t, j := 0, 0; n != 1; j++ {
for t = 0; n%primes[j] == 0; {
n /= primes[j]
t++
}
d *= t + 1
}
if d > limit {
ans = i * (i + 1) / 2
break
}
}
return ans
}
func E3() uint64 {
n, res := uint64(600851475143), uint64(0)
nf := float64(n)
primes := utils.Primes(int(math.Sqrt(nf)))
for _, p := range primes {
for n%uint64(p) == 0 {
n /= uint64(p)
res = uint64(p)
}
}
return res
}
func E49() string {
primes := utils.Primes(10000)
var a, b, c int
for i := 0; i < len(primes); i++ {
for j := i + 1; j < len(primes); j++ {
if utils.ArePermutations(primes[i], primes[j]) {
k := 2*primes[j] - primes[i]
if utils.IsPrime(k) && utils.ArePermutations(primes[i], k) {
a, b, c = primes[i], primes[j], k
}
}
}
}
return fmt.Sprintf("%d%d%d", a, b, c)
}
func E124() int {
const upto = 100000
primes := utils.Primes(upto)
rad := make(TupleArray, upto+1)
for i := 1; i <= upto; i++ {
rad[i][0], rad[i][1] = i, i
}
for _, i := range primes {
for k := 2; utils.Pow(i, k) <= upto && utils.Pow(i, k) > 0; k++ {
for j := utils.Pow(i, k); j <= upto; j += utils.Pow(i, k) {
rad[j][1] /= i
}
}
}
sort.Sort(rad)
return rad[10000][0]
}