/**
 * Build a map linking numbers to their dividors lists
 */
def dividors(upto) {
	def returned = new TreeMap()
	for(root in 1G..upto) {
		def increment = 1G
		def value
		while((value = root*increment)<upto) {
			if(!returned.containsKey(value)) {
				returned.put(value, new TreeSet())
				returned[value] << 1G
			}
			if(value>root) returned[value].add(root)
			if(value>increment) returned[value].add(increment)
			increment++
		}
	}
	return returned
}

def dividorsSums(upto) {
	def divides = dividors(upto)
//	println divides
	def sums = new TreeMap()
	divides.each { k, v ->
		sums[k] = v.sum()
	}
	return sums
}

def amicable(upto) {
	def sums = dividorsSums(upto)
//	println sums
	def amicableList = []
	sums.each {k, v ->
		if(sums[v]==k && k!=v)
			amicableList << k
	}
	return amicableList
}

long start = System.currentTimeMillis();

// def amicables = amicable(300G)
def amicables = amicable(10000G)
println amicables
println amicables.sum()

long end = System.currentTimeMillis();
println "duration "+((end-start)/1000.0)+" s";