/
p12.go
84 lines (65 loc) · 1.39 KB
/
p12.go
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/*
The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that 28 is the first triangle number to have over five divisors.
What is the value of the first triangle number to have over five hundred divisors?
*/
package main
import (
"fmt"
"utils"
)
var primes []uint64
func init() {
primes = utils.PrimesUpTo(15000)
}
func main() {
// Start at the 500th triangle number.
var triangle, n uint64 = 125250, 500
for {
factors := factor(triangle)
divisors := countDivisors(factors)
if divisors > 500 {
fmt.Printf("%d with factors %v has %d divisors", triangle, factors, divisors)
break
} else {
n++
triangle += n
}
}
}
func factor(n uint64) []uint64 {
if n == 1 {
return []uint64{}
}
for i := 0; primes[i] <= n; i++ {
p := primes[i]
if n%p == 0 {
return append(factor(n/p), p)
}
}
return nil
}
func countDivisors(factors []uint64) int {
exp := make(map[uint64]int)
for _, prime := range factors {
e, ok := exp[prime]
if !ok {
e = 0
}
exp[prime] = e + 1
}
divisors := 1
for _, e := range exp {
divisors *= e + 1
}
return divisors
}