Calculate sums of divisors using new sieves.

Author: strelec

021.scala

@@ -1,8 +1,10 @@
-val sieve = helpers.Sieve(100)
+val N = 10000 - 1
 
-val result = (2 until 10000).filter { i =>
-	val other = (sieve.sumOfDivisors(i) - i).toInt
-	i != other && i == sieve.sumOfDivisors(other) - other
+val sieve = sieves.DivisorSum(3 * N)
+
+val result = (2 to N).filter { i =>
+	val other = sieve(i) - i
+	i != other && i == sieve(other) - other
 }
 
 println(result.sum)

023.scala

@@ -1,12 +1,14 @@
 import scala.collection.Searching._
 
-val sieve = helpers.Sieve(168)
+val N = 28123
 
-val abundant = (1 to 28123).filter( i =>
-	sieve.sumOfDivisors(i) > 2*i
+val sieve = sieves.DivisorSum(N)
+
+val abundant = (1 to N).filter( i =>
+	sieve(i) > 2*i
 )
 
-val result = (1 to 28123).filter( i =>
+val result = (1 to N).filter( i =>
 	abundant.takeWhile(_ < i).forall( j =>
 		abundant.search(i - j) match {
 			case Found(_) => false

095.scala

@@ -1,5 +1,5 @@
 val N = 1000000
-val sieve = helpers.Sieve(1000)
+val sieve = sieves.DivisorSum(N)
 
 var seen = Set(1)
 var longest = -1
@@ -12,7 +12,7 @@ var result = 0
 		seen += i
 		step += 1
 		chain += i -> step
-		i = sieve.sumOfDivisors(i).toInt - i
+		i = sieve(i) - i
 	}
 	if (chain.contains(i)) {
 		val length = step - chain(i) + 1

Helpers.scala

@@ -51,24 +51,6 @@ case class Sieve(n: Int) {
 
 
 
-	def sumOfDivisors(num: Int): Long = {
-		var n = num
-		var result = 1L
-		primes.takeWhile( p =>
-			n != 1 && p*p <= n
-		).foreach { p =>
-			var cur = p
-			while(n % p == 0) {
-				n /= p
-				cur *= p
-			}
-			if (cur != p)
-				result *= (cur - 1)/(p - 1)
-		}
-		if (n != 1)
-			result *= (n.toLong*n - 1)/(n - 1)
-		result
-	}
 
 	def numberOfDivisors(num: Int, power: Int = 1): Int = {
 		var n = num