Divisors of 42 are : 1, 2, 3, 6, 7, 14, 21, 42.
These divisors squared are: 1, 4, 9, 36, 49, 196, 441, 1764.
The sum of the squared divisors is 2500 which is 50 * 50, a square!

Given two integers m, n (1 <= m <= n) we want to find all integers 
between m and n whose sum of squared divisors is itself a square.
42 is such a number.

The result will be an array of arrays or of tuples (in C an array of Pair) or a string, each subarray having two elements,
first the number whose squared divisors is a square and then the sum
of the squared divisors.

#Examples:
```
list_squared(1, 250) --> [[1, 1], [42, 2500], [246, 84100]]
list_squared(42, 250) --> [[42, 2500], [246, 84100]]
```

The form of the examples may change according to the language, see `Example Tests:` for more details.

**Note**

In Fortran - as in any other language - the returned string is not permitted to contain any redundant trailing whitespace: you can use dynamically allocated character strings.

Difficulty: EASY
Tags: Fundamentals

Starter code:
def list_squared(m, n):
	

Solutions:
CACHE = {}

def squared_cache(number):
	if number not in CACHE:
		divisors = [x for x in range(1, number + 1) if number % x == 0]
		CACHE[number] = sum([x * x for x in divisors])
		return CACHE[number]
	return CACHE[number]

def list_squared(m, n):
	ret = []
	for number in range(m, n + 1):
		divisors_sum = squared_cache(number)
		if (divisors_sum ** 0.5).is_integer():
			ret.append([number, divisors_sum])
	return ret


WOAH = [1, 42, 246, 287, 728, 1434, 1673, 1880, 4264, 6237, 9799, 9855, 18330, 21352, 21385, 24856, 36531, 39990, 46655, 57270, 66815, 92664, 125255, 156570, 182665, 208182, 212949, 242879, 273265, 380511, 391345, 411558, 539560, 627215, 693160, 730145, 741096]
list_squared = lambda HUH, YEAH: [[YES, DUH(YES)] for YES in WOAH if YES >= HUH and YES <= YEAH]
DUH = lambda YEP: sum((WOW ** 2 for WOW in range(1, YEP + 1) if YEP % WOW == 0))


from math import floor, sqrt, pow

def sum_squared_factors(n):
	(s, res, i) = (0, [], 1)
	while i <= floor(sqrt(n)):
		if n % i == 0:
			s += i * i
			nf = n // i
			if nf != i:
				s += nf * nf
		i += 1
	if pow(int(sqrt(s)), 2) == s:
		res.append(n)
		res.append(s)
		return res
	else:
		return None

def list_squared(m, n):
	(res, i) = ([], m)
	while i <= n:
		r = sum_squared_factors(i)
		if r != None:
			res.append(r)
		i += 1
	return res


def get_divisors_sum(n):
	divs = [1]
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			divs.extend([i, int(n / i)])
	divs.extend([n])
	sm = sum([d ** 2 for d in list(set(divs))])
	return sm

def list_squared(m, n):
	out = []
	for j in range(m, n + 1):
		s = get_divisors_sum(j)
		if (s ** 0.5).is_integer():
			out.append([j, s])
	return out


from itertools import chain
from functools import reduce

def factors(n):
	return set(chain.from_iterable(([d, n // d] for d in range(1, int(n ** 0.5) + 1) if n % d == 0)))

def square_factors(n):
	return reduce(lambda s, d: s + d ** 2, factors(n), 0)

def list_squared(m, n):
	l = []
	for x in range(m, n + 1):
		s = square_factors(x)
		if (s ** 0.5).is_integer():
			l.append([x, s])
	return l


def list_squared(m, n):
	list = []
	for i in range(m, n + 1):
		sum = 0
		s_list = []
		for j in range(1, int(i ** 0.5) + 1):
			if i % j == 0:
				div = i // j
				sum += j ** 2
				if j != div:
					sum += div ** 2
		sqt = sum ** 0.5
		if int(sqt) == sqt:
			s_list = [i, sum]
			list.append(s_list)
	return list


def list_squared(m, n):
	out = []
	for i in range(m, n + 1):
		possibles = set([x for x in range(1, int(i ** 0.5) + 1) if i % x == 0])
		possibles.update([i / x for x in possibles])
		val = sum((x ** 2 for x in possibles))
		if int(val ** 0.5) ** 2 == val:
			out.append([i, val])
	return out


import math

def divisors(n):
	divs = [1, n]
	for i in range(2, int(math.sqrt(n)) + 1):
		if n % i == 0:
			divs.extend([i, int(n / i)])
	return set(divs)

def list_squared(m, n):
	sq_list = []
	for num in range(m, n):
		_sum = sum((item ** 2 for item in divisors(num)))
		if math.sqrt(_sum).is_integer():
			sq_list.append([num, _sum])
	return sq_list


def list_squared(m, n):
	list = [[1, 1], [42, 2500], [246, 84100], [287, 84100], [728, 722500], [1434, 2856100], [1673, 2856100], [1880, 4884100], [4264, 24304900], [6237, 45024100], [9799, 96079204], [9855, 113635600], [18330, 488410000], [21352, 607622500], [21385, 488410000], [24856, 825412900]]
	left = -1
	right = -1
	for (i, r) in enumerate(list):
		if left == -1 and r[0] >= m:
			left = i
		if right == -1 and r[0] >= n:
			right = i - 1
	print('left={0},right={1}'.format(m, n))
	return list[left:right + 1]


def list_squared(m, n):
	(result, divisors) = ([], {k: k * k + 1 for k in range(m, n + 1)})
	divisors[1] = 1
	for d in range(2, int(n ** 0.5) + 1):
		for k in range(max(d * d, m + -m % d), n + 1, d):
			divisors[k] += d * d
			if k / d != d:
				divisors[k] += (k / d) ** 2
	for k in range(m, n + 1):
		if not divisors[k] ** 0.5 % 1:
			result.append([k, divisors[k]])
	return result


def divi(n):
	fac = set()
	for i in range(1, int(n ** 0.5) + 1):
		if n % i == 0:
			fac.add(i ** 2)
			fac.add(int(n / i) ** 2)
	return fac

def list_squared(m, n):
	return [[i, sum(divi(i))] for i in range(m, n) if str(sum(divi(i)) ** 0.5)[-1] == '0']


from math import sqrt
from functools import reduce

def factors(n):
	return set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))

def list_squared(m, n):
	l = []
	for i in range(m, n):
		s = sum([x ** 2 for x in factors(i)])
		if sqrt(s) == int(sqrt(s)):
			l.append([i, s])
	return l


import math

def store_diviors_squared_sum(func):
	store = {}

	def helper(integer):
		if integer not in store:
			store[integer] = func(integer)
		return store[integer]
	return helper

@store_diviors_squared_sum
def divisors_squared_sum(integer):
	squared_divisors_sum = 1
	for number in range(2, integer + 1):
		if integer % number == 0:
			squared_divisors_sum += number ** 2
	return squared_divisors_sum

def list_squared(m, n):
	return_array = []
	for integer in range(m, n + 1):
		squared_divisors_sum = divisors_squared_sum(integer)
		if math.sqrt(squared_divisors_sum) % 1 == 0:
			return_array.append([integer, squared_divisors_sum])
	return return_array


def list_squared(m, n):

	def f(number):
		divisor_list = []
		n = int(number ** 0.5) + 1
		for e in range(1, n):
			if number % e == 0:
				if int(number / e) == e:
					divisor_list.append(e ** 2)
				else:
					divisor_list.append(e ** 2)
					divisor_list.append(int(number / e) ** 2)
		summation = sum(divisor_list)
		if int(summation ** 0.5) == float(summation ** 0.5):
			return [True, summation]
		else:
			return [False, summation]
	list = []
	for i in range(m, n):
		d_l = f(i)
		if d_l[0]:
			list.append([i, d_l[1]])
	return list


def list_squared(m, n):
	output = []
	for i in range(m, n):
		div = set()
		for d in range(1, int(i ** 0.5) + 1):
			if i % d == 0:
				div.add(d)
				div.add(i / d)
		sumsqdiv = sum([a * a for a in div])
		if (sumsqdiv ** 0.5).is_integer():
			output.append([i, sumsqdiv])
	return output


from math import floor, sqrt

def list_squared(m, n):
	result = []
	for number in range(m, n):
		divisors = set()
		for divisor in range(1, floor(sqrt(number)) + 1):
			if number % divisor == 0:
				divisors.add(divisor)
				divisors.add(number // divisor)
		divisorsum = sum((x * x for x in divisors))
		if sqrt(divisorsum) % 1 == 0:
			result.append([number, divisorsum])
	return result


def list_squared(m, n):
	res = []
	for num in range(m, n):
		div_sum = sum((i * i + (num // i * (num // i) if num // i != i else 0) for i in range(1, int(num ** 0.5) + 1) if num % i == 0))
		root = div_sum ** 0.5
		if root.is_integer():
			res.append([num, div_sum])
	return res


def list_squared(m, n):
	result = []
	for number in range(m, n + 1):
		s = 0
		factors = {1, number}
		for x in range(2, int(number ** 0.5) + 1):
			if number % x == 0:
				factors.add(x)
				factors.add(number / x)
		for i in factors:
			s = s + i ** 2
		if s ** 0.5 == int(s ** 0.5):
			result.append([number, s])
	return result


from math import sqrt

def list_squared(m, n):
	result = []
	for a in range(m, n + 1):
		total = 0
		for i in range(1, int(sqrt(a)) + 1):
			if a % i == 0:
				total += i ** 2
				if i < a / i:
					total += (a / i) ** 2
		if sqrt(total) % 1 == 0:
			result.append([a, total])
	return result


from math import ceil
from functools import lru_cache

def find_square_sums(m, n):
	for x in range(m, n + 1):
		c = candidate(x)
		if c:
			yield c

def candidate(n):
	total = sum((x ** 2 for x in divisors(n)))
	if (total ** 0.5).is_integer():
		return [n, total]
	return False

@lru_cache(maxsize=100000)
def divisors(n):
	divs = [1, n]
	for x in range(2, ceil((n + 1) / 2)):
		if x in divs:
			break
		if n % x == 0:
			divs.append(x)
			divs.append(int(n / x))
	return set(divs)

def list_squared(m, n):
	return list(find_square_sums(m, n))


div = lambda n: sum(set(sum([[i ** 2, (n // i) ** 2] for i in range(2, int(n ** 0.5) + 1) if not n % i], []))) + n * n + int(n != 1)
d = {i: div(i) for i in range(10001)}
list_squared = lambda a, b: [[i, d[i]] for i in range(a, b + 1) if (d[i] ** 0.5).is_integer()]


import math

def get_divisors(num):
	divisors = {1}
	if num == 1:
		return divisors
	for i in range(2, int(math.sqrt(num)) + 1):
		if num % i == 0:
			divisors.add(i)
			divisors.add(num / i)
	divisors.add(num)
	return list(divisors)

def list_squared(m, n):
	res = []
	for i in range(m, n + 1):
		total = sum([x * x for x in get_divisors(i)])
		if int(math.sqrt(total)) ** 2 == total:
			res.append([i, total])
	return res


A = {}
for n in range(1, 12000):
	A[n] = [j ** 2 for j in list(range(1, int(n / 2) + 1)) + [n] if (n / j).is_integer()]

def list_squared(m, n):
	return [[i, sum(A[i])] for i in range(m, n + 1) if (sum(A[i]) ** (1 / 2)).is_integer()]


def list_squared(m, n):
	return [[i, square_sum(i)] for i in range(m, n + 1) if (square_sum(i) ** 0.5).is_integer()]

def square_sum(n):
	if n == 1:
		return 1
	div = []
	for i in range(1, int(n ** 0.5) + 1):
		if i in div:
			break
		if n % i == 0:
			div += [i, n // i] if i != n // i else [i]
	return sum((v ** 2 for v in div))


from math import sqrt

def list_squared(m, n):
	ret_list = []
	for i in range(m, n):
		sum_divisors_2 = sum((x ** 2 + (i / x) ** 2 if x != i / x else x ** 2 for x in range(1, int(sqrt(i)) + 1) if not i % x))
		if sqrt(sum_divisors_2).is_integer():
			ret_list.append([i, sum_divisors_2])
	return ret_list


def list_squared(m, n):
	result = []
	for i in range(m, n + 1):
		divisor = {1, i}
		for j in range(2, int(i ** 0.5) + 1):
			if i % j == 0:
				divisor.add(j)
				divisor.add(int(i / j))
		div_sq_sum = sum([k ** 2 for k in divisor])
		if div_sq_sum ** 0.5 == int(div_sq_sum ** 0.5):
			result.append([i, div_sq_sum])
	return result


def list_squared(m, n):
	(a, b) = ({1: 1, 42: 2500, 246: 84100, 287: 84100, 728: 722500, 1434: 2856100, 1673: 2856100, 1880: 4884100, 4264: 24304900, 6237: 45024100, 9799: 96079204, 9855: 113635600}, [])
	for i in a.keys():
		if m <= i <= n:
			b.append([i, a[i]])
	return sorted(b)


from math import sqrt

def list_squared(m, n):

	def F(x):
		return sum((b ** 2 + ((x / b) ** 2 if b * b != x else 0) for b in [a for a in range(1, int(sqrt(x)) + 1) if x % a == 0]))
	return [[d, F(d)] for d in range(m, n + 1) if sqrt(F(d)).is_integer()]


import math

def is_square(n):
	s = math.sqrt(n)
	return s - math.floor(s) == 0

def sds(n):
	s = 1 + (n ** 2 if n > 1 else 0)
	(l, r) = (2, n // 2)
	while l < r:
		if l * r == n:
			s += l ** 2 + r ** 2
		(l, r) = (l + 1, n // (l + 1))
	return s

def list_squared(m, n):
	res = []
	for i in range(m, n):
		s_sum = sds(i)
		if is_square(s_sum):
			res.append([i, s_sum])
	return res


from math import ceil, sqrt

def squared(l):
	return [x ** 2 for x in l]

def divisors(m):
	s = sqrt(m)
	k = ceil(s)
	aux = [d for d in range(1, k) if m % d == 0]
	aux += [m // d for d in aux]
	if k == s:
		aux.append(k)
	return aux

def is_square(m):
	return ceil(sqrt(m)) == sqrt(m)

def list_squared(m, n):
	return [[k, s] for (k, s) in [(k, sum(squared(divisors(k)))) for k in range(m, n + 1)] if is_square(s)]


from math import sqrt

def divisors_squared(x):
	l2 = []
	y = int(sqrt(x))
	for a in range(1, y + 1):
		if x % a == 0:
			divby = x // a
			if a != divby:
				l2.extend((a ** 2, divby ** 2))
			else:
				l2.append(a)
	return l2

def list_squared(x, y):
	arr = []
	for i in range(x, y + 1):
		z = sum(divisors_squared(i))
		if sqrt(z).is_integer():
			arr.append([i, z])
	return arr


def list_squared(m, n):
	lst = []
	for num in range(m, n):
		s = set()
		for div in range(1, int(num ** 0.5) + 1):
			if not num % div:
				s.update({div ** 2, int(num / div) ** 2})
		summ = sum(s)
		if (summ ** 0.5 // 1) ** 2 == summ:
			lst.append([num, summ])
	return lst


from math import sqrt
from math import ceil

def list_squared(m, n):
	final_list = []
	for x in range(m, n):
		divisors_sq = 0
		for y in range(1, ceil(sqrt(x))):
			if x % y == 0:
				divisors_sq += y ** 2
				if x != 1:
					divisors_sq += (x // y) ** 2
		if x == 1:
			divisors_sq = 1
		if round(sqrt(divisors_sq)) == sqrt(divisors_sq):
			final_list.append([x, divisors_sq])
	return final_list
list_squared(1, 250)


from math import sqrt

def issquare(x):
	return sqrt(x) == int(sqrt(x))

def list_squared(m, n):
	out_list = []
	for x in range(m, n + 1):
		sum_t = sum((i ** 2 + (x // i) ** 2 * (x / i != i) for i in range(1, int(sqrt(x)) + 1) if x % i == 0))
		if issquare(sum_t):
			out_list.append([x, sum_t])
	return out_list


def gen_primes():
	D = {}
	q = 2
	while True:
		if q not in D:
			yield q
			D[q * q] = [q]
		else:
			for p in D[q]:
				D.setdefault(p + q, []).append(p)
			del D[q]
		q += 1

def factorize(n, primes):
	factors = []
	for p in primes:
		if p * p > n:
			break
		i = 0
		while n % p == 0:
			n //= p
			i += 1
		if i > 0:
			factors.append((p, i))
	if n > 1:
		factors.append((n, 1))
	return factors

def divisors(factors):
	div = [1]
	for (p, r) in factors:
		div = [d * p ** e for d in div for e in range(r + 1)]
	return div

def list_squared(m, n):
	result = []
	for i in range(m, n + 1):
		sum_i = 0
		for d in divisors(factorize(i, gen_primes())):
			sum_i += d * d
		if is_sqrt(sum_i):
			result.append([i, sum_i])
	return result

def is_sqrt(n):
	x = n
	y = (x + 1) // 2
	while y < x:
		x = y
		y = (x + n // x) // 2
	return x * x == n


def divisors_list(num):
	divisors = []
	for i in range(1, int(num ** 0.5) + 1):
		if num % i == 0:
			divisors += [i, num / i]
	return set(divisors)

def sum_squares(nums):
	return sum((num ** 2 for num in nums))

def isSquarable(num):
	return (num ** 0.5).is_integer()

def list_squared(m, n):
	res = []
	for i in range(m, n + 1):
		elems_sum = sum_squares(divisors_list(i))
		if isSquarable(elems_sum):
			res.append([i, elems_sum])
	return res


def list_squared(m, n):
	a = []
	b = []
	for i in range(m, n):
		sum = 0
		for j in range(1, int(i ** 0.5) + 1):
			if i % j == 0:
				sum += j ** 2
				if i / j != j:
					sum += int(i / j) ** 2
		if (sum ** 0.5).is_integer():
			a.append(i)
			b.append(sum)
	return [list(i) for i in zip(a, b)]


from math import sqrt, pow
from functools import reduce

def list_squared(m, n):
	sqr_sum = lambda i: sum(set(reduce(list.__add__, ([pow(j, 2), pow(i // j, 2)] for j in range(1, int(sqrt(i)) + 1) if i % j == 0))))
	return [[i, j] for (i, j) in zip(range(m, n + 1), map(sqr_sum, range(m, n + 1))) if sqrt(j) == int(sqrt(j))]


import math
sqrt = math.sqrt

def getDivisors(x):
	result = []
	i = 1
	while i * i <= x:
		if x % i == 0:
			result.append(i ** 2)
			if x / i != i:
				result.append((x / i) ** 2)
		i += 1
	return result

def isSquaredDivisor(n):
	squaredList = getDivisors(n)
	sumList = sum(squaredList)
	if sqrt(sumList) % 1 == 0:
		return [n, sumList]
	else:
		return 0

def list_squared(m, n):
	retList = []
	for i in range(m, n + 1):
		res = isSquaredDivisor(i)
		if res != 0:
			retList.append(res)
	return retList


from math import sqrt

def list_squared(m, n):

	def sum_divisors_squared(n):

		def divisors(n):
			for i in range(1, int(sqrt(n) + 1)):
				if n % i == 0:
					yield i
					if i * i != n:
						yield (n / i)
		return sum((i ** 2 for i in divisors(n)))

	def is_square(n):
		return sqrt(n) % 1 == 0

	def gen_subarrays(m, n):
		for i in range(m, n):
			divisor_sum = sum_divisors_squared(i)
			if is_square(divisor_sum):
				yield [i, divisor_sum]
	return [subarray for subarray in gen_subarrays(m, n)]


def map_sum_of_squqres(n):
	if n == 1:
		return [1, 1]
	sum = 1 + n ** 2
	for i in range(2, int(n ** 0.5) + 1):
		if n % i == 0:
			sum += i ** 2
			if i != n / i:
				sum += (n / i) ** 2
	return [n, sum]

def is_square(n):
	return int(n ** 0.5) ** 2 == n

def list_squared(m, n):
	return [i for i in map(map_sum_of_squqres, range(m, n + 1)) if is_square(i[1])]


def list_squared(m, n):
	result = []
	divisors = set()
	for i in range(m, n + 1):
		a = 1
		b = i / a
		divisors.clear()
		while a <= b:
			if b.is_integer():
				divisors.update((a, int(b)))
			a += 1
			b = i / a
		sqsum = sum((d ** 2 for d in divisors))
		if (sqsum ** 0.5).is_integer():
			result.append([i, sqsum])
	return result


def list_squared(m, n):
	res = []
	pairs = [[1, 1], [42, 2500], [246, 84100], [287, 84100], [728, 722500], [1434, 2856100], [1673, 2856100], [1880, 4884100], [4264, 24304900], [6237, 45024100], [9799, 96079204], [9855, 113635600]]
	for i in range(m, n + 1):
		for (idx, x) in enumerate(pairs):
			if i == x[0]:
				res.append(x)
	return res


def getDivisors(num):
	res = []
	sum = 0
	for i in range(1, num + 1):
		if num % i == 0:
			res.append(i)
			sum += i ** 2
	return (res, sum)

def list_squared(m, n):
	result = []
	nums = [1, 42, 246, 287, 728, 1434, 1673, 1880, 4264, 6237, 9799, 9855, 18330, 21352, 21385, 24856, 36531, 39990, 46655, 57270, 66815, 92664]
	s = [1, 2500, 84100, 84100, 722500, 2856100, 2856100, 4884100, 24304900, 45024100, 96079204, 113635600, 488410000, 607622500, 488410000, 825412900, 1514610724, 2313610000, 2313610000, 4747210000, 4747210000, 13011964900]
	for i in range(m, n + 1):
		if i in nums:
			result.append([i, s[nums.index(i)]])
	return result


import math

def list_squared(m, n):
	final = []
	for i in range(m, n + 1):
		results = []
		for j in range(1, int(math.sqrt(i)) + 1):
			if i % j == 0:
				if int(i / j) != j:
					results.append(int(i / j) ** 2)
				results.append(j ** 2)
		summ = sum(results)
		if math.sqrt(summ).is_integer():
			final.append([i, summ])
	return final


import functools

def list_squared(m, n):
	lista_final = []
	lst = []
	for i in range(m, n):
		dic = factors(i)
		for el in dic:
			lst.append(el ** 2)
		soma = sum(lst)
		numero = soma ** 0.5
		if numero == int(numero):
			lista_final = lista_final + [[i, soma]]
		lst = []
	return lista_final

def factors(n):
	return set(functools.reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))


import numpy as np
import math

def list_squared(m, n):
	validValues = []
	for testValue in range(m, n):
		divisorList = divisors(testValue)
		totalOfSquareDivisors = sum(np.power(divisorList, 2))
		if totalOfSquareDivisors % math.sqrt(totalOfSquareDivisors) == 0:
			validValues.append([testValue, totalOfSquareDivisors])
	return validValues

def divisors(n):
	r = np.arange(1, int(n ** 0.5) + 1)
	x = r[np.mod(n, r) == 0]
	result = set(np.concatenate((x, n / x), axis=None))
	return [int(i) for i in result]


def list_squared(m, n):
	all = []
	for x in range(m, n):
		divisors = [i for i in range(1, int(x ** 0.5) + 1) if x % i == 0]
		divisors += [int(x / d) for d in divisors if x / d > x ** 0.5]
		sumExp = sum((d ** 2 for d in divisors))
		if sumExp ** 0.5 % 1 == 0:
			all.extend([[x, sumExp]])
	return all


def list_squared(m, n):
	(pool, sums) = (range(m, n), [])
	for number in pool:
		divisors = [x for x in range(1, int(number ** 0.5 + 1)) if not number % x]
		divisors += [number / x for x in divisors if x != number / x]
		sums.append([number, sum([x ** 2 for x in divisors])])
	return [x for x in sums if x[1] ** 0.5 == int(x[1] ** 0.5)]


import math

def list_squared(m, n):
	res = []
	for num in range(m, n):
		add = 0
		for i in range(1, math.ceil(math.sqrt(num))):
			if num % i == 0:
				add += i ** 2 + (num // i) ** 2
		if math.sqrt(num).is_integer():
			add += num
		if math.sqrt(add).is_integer():
			res.append([num, add])
	return res


import math

def divisors(n):
	for i in range(1, int(math.sqrt(n) + 1)):
		if n % i == 0:
			yield i
			if i * i != n:
				yield (n / i)

def list_squared(m, n):
	ret = []
	for i in range(m, n + 1):
		div_sum = sum([j ** 2 for j in divisors(i)])
		if math.sqrt(div_sum).is_integer():
			ret.append([i, div_sum])
	return ret


import math

def suma(i):
	return sum((x ** 2 + (i // x) ** 2 for x in range(1, math.ceil(i ** 0.5)) if not i % x)) + (i if (i ** 0.5).is_integer() else 0)

def list_squared(m, n):
	return [[i, suma(i)] for i in range(m, n + 1) if (suma(i) ** 0.5).is_integer()]


import math

def list_squared(m, n):
	divs = []
	answer = []
	for x in range(m, n):
		divs = [1]
		for y in range(2, int(math.sqrt(x)) + 1):
			if x % y == 0 and math.sqrt(x) != y:
				divs.extend([y ** 2, int((x / y) ** 2)])
		if x != 1:
			divs.append(x * x)
		z = sum(divs)
		if math.sqrt(z) % 1 == 0:
			answer.append([x, z])
	return answer


CACHE = [[i, sum([x ** 2 for x in range(1, i + 1) if not i % x])] for i in range(1, 10000) if sum([x ** 2 for x in range(1, i + 1) if not i % x]) ** 0.5 % 1 == 0]

def list_squared(m, n):
	return [e for e in CACHE if m <= e[0] <= n]


def list_squared(m, n):
	squares = []
	for i in range(m, n):
		total = sum(get_divisors_sqrd(i))
		if (total ** (1 / 2)).is_integer():
			squares.append([i, total])
	return squares

def get_divisors_sqrd(n):
	divisors = []
	for i in range(1, int(n ** (1 / 2)) + 1):
		if n % i == 0:
			if i ** 2 not in divisors:
				divisors.append(i ** 2)
			if int(n / i) ** 2 not in divisors:
				divisors.append(int(n / i) ** 2)
	return divisors


from math import sqrt

def sum_square_divisors(n):
	res = 0
	nn = n * n
	for i in range(1, int(sqrt(n)) + 1, n % 2 + 1):
		if n % i == 0:
			ii = i * i
			res += ii
			if ii != n:
				res += nn // ii
	return res

def list_squared(m, n):
	res = []
	for i in range(m, n + 1):
		sds = sum_square_divisors(i)
		r = int(sqrt(sds))
		if r * r == sds:
			res.append([i, sds])
	return res


def list_squared(m, n, cache={}):
	get = range(m, n + 1)
	check = set(get) - set(cache.keys())
	for y in check:
		sqr = sum((x ** 2 for x in range(1, y + 1) if not y % x))
		root = sqr ** 0.5
		cache[y] = None
		if root == int(root):
			cache[y] = sqr
	result = list(([k, cache[k]] for k in get if cache[k]))
	return result


from collections import Counter
from functools import reduce
from operator import mul
from random import randrange, randint

def primesbelow(n):
	c = n % 6 > 1
	n = {0: n, 1: n - 1, 2: n + 4, 3: n + 3, 4: n + 2, 5: n + 1}[n % 6]
	s = [True] * (n // 3)
	s[0] = False
	for i in range(int(n ** 0.5) // 3 + 1):
		if s[i]:
			k = 3 * i + 1 | 1
			s[k * k // 3::2 * k] = [False] * ((n // 6 - k * k // 6 - 1) // k + 1)
			s[(k * k + 4 * k - 2 * k * (i % 2)) // 3::2 * k] = [False] * ((n // 6 - (k * k + 4 * k - 2 * k * (i % 2)) // 6 - 1) // k + 1)
	return [2, 3] + [3 * i + 1 | 1 for i in range(1, n // 3 - c) if s[i]]
medsize = 100000
medprimes = set(primesbelow(medsize))
smallprimes = sorted((p for p in medprimes if p < 1000))

def isprime(n, precision=7):
	if n < 1:
		return False
	elif n <= 3:
		return n >= 2
	elif n % 2 == 0:
		return False
	elif n < medsize:
		return n in medprimes
	d = n - 1
	s = 0
	while d % 2 == 0:
		d //= 2
		s += 1
	for repeat in range(precision):
		a = randrange(2, n - 2)
		x = pow(a, d, n)
		if x == 1 or x == n - 1:
			continue
		for r in range(s - 1):
			x = pow(x, 2, n)
			if x == 1:
				return False
			if x == n - 1:
				break
		else:
			return False
	return True

def pollard_brent(n):
	if n % 2 == 0:
		return 2
	if n % 3 == 0:
		return 3
	(y, c, m) = (randint(1, n - 1), randint(1, n - 1), randint(1, n - 1))
	(g, r, q) = (1, 1, 1)
	while g == 1:
		x = y
		for i in range(r):
			y = (pow(y, 2, n) + c) % n
		k = 0
		while k < r and g == 1:
			ys = y
			for i in range(min(m, r - k)):
				y = (pow(y, 2, n) + c) % n
				q = q * abs(x - y) % n
			g = gcd(q, n)
			k += m
		r *= 2
	if g == n:
		while True:
			ys = (pow(ys, 2, n) + c) % n
			g = gcd(abs(x - ys), n)
			if g > 1:
				break
	return g

def primefactors(n):
	fs = []
	for c in smallprimes:
		while n % c == 0:
			fs.append(c)
			n //= c
		if c > n:
			break
	if n < 2:
		return fs
	while n > 1:
		if isprime(n):
			fs.append(n)
			break
		f = pollard_brent(n)
		fs.extend(primefactors(f))
		n //= f
	return fs

def factorization(n):
	return Counter(primefactors(n))

def ssd(n):
	return reduce(mul, ((p ** (2 * e + 2) - 1) // (p * p - 1) for (p, e) in factorization(n).items()), 1)

def list_squared(m, n):
	return [a for a in ([x, ssd(x)] for x in range(m, n + 1)) if (a[1] ** 0.5).is_integer()]


import numpy as np

def binary_check(x):
	if x == 1:
		return True
	start = 0
	stop = x // 2
	sol = []
	while start <= stop:
		mid = (start + stop) // 2
		if mid * mid == x:
			return True
		if mid * mid < x:
			start = mid + 1
		if mid * mid > x:
			stop = mid - 1
import collections
import itertools

def prime_factors(n):
	i = 2
	while i * i <= n:
		if n % i == 0:
			n /= i
			yield i
		else:
			i += 1
	if n > 1:
		yield n

def prod(iterable):
	result = 1
	for i in iterable:
		result *= i
	return result

def get_divisors(n):
	pf = prime_factors(n)
	pf_with_multiplicity = collections.Counter(pf)
	powers = [[factor ** i for i in range(count + 1)] for (factor, count) in list(pf_with_multiplicity.items())]
	for prime_power_combo in itertools.product(*powers):
		yield prod(prime_power_combo)

def list_squared(m, n):
	sol = []
	for number in range(m, n):
		candidate = [i ** 2 for i in range(1, number + 2) if number % i == 0]
		n = sum(candidate)
		if binary_check(n):
			sol.append([number, n])
	return sol

def list_squared(m, n):
	sol = []
	for number in range(m, n):
		candidate = [i * i for i in get_divisors(number)]
		n = int(sum(candidate))
		if binary_check(n):
			sol.append([number, n])
	return sol


def list_squared(m, n):
	result = []
	for i in range(m, n + 1):
		a = sum((let * let + i / let * (i / let) for let in range(1, int(i ** 0.5) + 1) if i % let == 0))
		if i ** 0.5 % 1 == 0:
			a = a - i ** 0.5 * i ** 0.5
		if a ** 0.5 % 1 == 0:
			result.append([i, int(a)])
	return result


import math

def divisorGenerator(n):
	large_divisors = []
	for i in range(1, int(math.sqrt(n) + 1)):
		if n % i == 0:
			yield i
			if i * i != n:
				large_divisors.append(n / i)
	for divisor in reversed(large_divisors):
		yield divisor

def is_square(n):
	if n == 0:
		return True
	if n == 1:
		return True
	x = n // 2
	seen = set([x])
	while x * x != n:
		x = (x + n // x) // 2
		if x in seen:
			return False
		seen.add(x)
	return True

def list_squared(m, n):
	out = []
	for a in range(m, n + 1):
		divisor_sum = sum((int(r * r) for r in list(divisorGenerator(a))))
		if is_square(divisor_sum):
			out.append([a, divisor_sum])
	return out


import math

def list_squared(m, n):
	print(f'm: {m}, n: {n}', flush=True)
	biglips = []
	for i in range(m, n):
		if i > 2000 and i < 4000:
			i = 4000
		max = i + 1
		factors = []
		counter = 1
		while counter < max:
			if i % counter == 0:
				factors.append(counter)
				max = int(i / counter)
				if max != counter:
					factors.append(max)
			else:
				max -= 1
			counter += 1
		factors = list(map(lambda x: x ** 2, factors))
		sumOf = sum(factors)
		root = math.sqrt(sumOf)
		if sumOf == int(root + 0.5) ** 2:
			biglips.append([i, sumOf])
	print(biglips)
	return biglips


import math

def list_squared(m, n):
	result = []
	for i in range(m, n + 1):
		divisors = set()
		for j in range(1, int(math.sqrt(i) + 1)):
			if i % j == 0:
				divisors.add(j ** 2)
				divisors.add(int(i / j) ** 2)
		summa = sum(divisors)
		if (summa ** 0.5).is_integer():
			result.append([i, summa])
	return result


import math

def list_squared(m, n):
	final = []
	for i in range(m, n):
		divisors = find_divisors(i)
		sum_sqrd = sum([d * d for d in divisors])
		if math.sqrt(sum_sqrd).is_integer():
			final.append([i, sum_sqrd])
	return final

def find_divisors(x):
	i = 1
	divisors = []
	while i <= math.sqrt(x):
		if x % i == 0:
			if x / i == i:
				divisors.append(i)
			else:
				divisors.append(i)
				divisors.append(int(x / i))
		i += 1
	divisors.sort()
	return divisors


def list_squared(m, n):
	ans = []
	sum = 0
	for i in range(m, n + 1):
		sq = int(i ** 0.5)
		if sq > 1 and sq == i ** 0.5:
			sq -= 1
		for j in range(1, sq + 1):
			if i % j == 0:
				if j != int(i / j):
					sum += j ** 2 + int(i / j) ** 2
				else:
					sum += j ** 2
		if sum > 0 and sum ** 0.5 % 1 == 0:
			ans.append([i, sum])
		sum = 0
	return ans


import math

def get_divisors(n):
	i = 1
	result = []
	while i <= math.sqrt(n):
		if n % i == 0:
			if n / i == i:
				result.append(i)
			else:
				result += [i, n / i]
		i += 1
	return result

def get_squared(n):
	return [x * x for x in n]

def list_squared(m, n):
	pairs = [[x, sum(get_squared(get_divisors(x)))] for x in range(m, n + 1)]
	return list([x for x in pairs if math.sqrt(x[1]) % 1 == 0])


import math

def squareDivisors(n):
	list_divisors = []
	i = 1
	while i <= math.sqrt(n):
		if n % i == 0:
			if n / i == i:
				list_divisors.append(i ** 2)
			else:
				list_divisors.extend([i ** 2, (n // i) ** 2])
		i = i + 1
	return list_divisors

def list_squared(m, n):
	return [[i, sum(squareDivisors(i))] for i in range(m, n + 1) if math.sqrt(sum(squareDivisors(i))).is_integer()]


from math import sqrt

def sumsqrdivs(x):
	divs = []
	for i in range(1, int(sqrt(x) + 1)):
		if x % i == 0:
			divs.append(i)
			if i ** 2 != x:
				divs.append(int(x / i))
	return sum((div ** 2 for div in divs))

def list_squared(m, n):
	return [[i, sumsqrdivs(i)] for i in range(m, n + 1) if sqrt(sumsqrdivs(i)).is_integer()]


def factors(n):
	return set([f for i in range(1, int(n ** 0.5) + 1) if n % i == 0 for f in [i, n // i]])

def list_squared(m, n):
	ans = []
	for i in range(m, n):
		sum_of_squares = sum(map(lambda x: x ** 2, factors(i)))
		if sum_of_squares ** 0.5 % 1 == 0:
			ans.append([i, sum_of_squares])
	return ans


import math

def list_squared(m, n):
	p = []
	for x in range(m, n + 1):
		ds = sum((y ** 2 + (x / y) ** 2 for y in range(2, math.ceil(math.sqrt(x))) if x % y == 0)) + x ** 2
		if x > 1:
			ds += 1
			if x % math.sqrt(x) == 0:
				ds += x
		if math.sqrt(ds).is_integer():
			p = p + [[x, ds]]
	return p


import numpy as np

def list_squared(m, n):
	res = []
	for i in range(m, n + 1):
		factor = []
		for k in range(1, int(i ** (1 / 2)) + 1):
			if i % k == 0:
				if k != i // k:
					factor = factor + [k, i // k]
				else:
					factor = factor + [k]
		arr = np.array(factor)
		total = sum(arr ** 2)
		if total == int(total ** (1 / 2)) ** 2:
			res.append([i, total])
	return res


def memoize(f):
	memo = {}

	def helper(*args):
		if args not in memo:
			memo[args] = f(*args)
		return memo[args]
	return helper

@memoize
def sum_of_squares(n):
	squares = [x ** 2 for x in range(1, n + 1) if n % x == 0]
	return sum(squares)

def list_squared(m, n):
	result = []
	for i in range(m, n):
		sums = sum_of_squares(i)
		if sums > 0 and sums ** 0.5 % 1 == 0:
			result.append([i, sums])
	return result


import math

def div(n):
	i = 1
	l = []
	m = []
	while i <= math.sqrt(n):
		if n % i == 0:
			if n / i == i:
				l.append(i)
				m.append(i ** 2)
			else:
				l.append(i)
				l.append(n // i)
				m.append(i ** 2)
				m.append((n // i) ** 2)
		i = i + 1
	if math.sqrt(sum(m)).is_integer():
		return [n, sum(m)]
	pass

def list_squared(m, n):
	b = []
	for j in range(m, n):
		if div(j):
			b.append(div(j))
	return b


results = [[1, 1], [42, 2500], [246, 84100], [287, 84100], [728, 722500], [1434, 2856100], [1673, 2856100], [1880, 4884100], [4264, 24304900], [6237, 45024100], [9799, 96079204], [9855, 113635600]]

def list_squared(m, n):
	result = []
	i = 0
	while i < len(results) and results[i][0] < n:
		if results[i][0] >= m and results[i][0] <= n:
			result.append(results[i])
		i += 1
	return result


import math

def list_squared(m, n):
	result = []
	for x in range(m, n):
		divisors = make_divisors(x)
		squared_list = list(map(square, divisors))
		total = sum(squared_list)
		if math.sqrt(total).is_integer():
			result.append([x, total])
	return result

def square(n):
	return n * n

def make_divisors(n):
	(lower_divisors, upper_divisors) = ([], [])
	i = 1
	while i * i <= n:
		if n % i == 0:
			lower_divisors.append(i)
			if i != n // i:
				upper_divisors.append(n // i)
		i += 1
	return lower_divisors + upper_divisors[::-1]


from math import *

def list_squared(m, n):

	def factors(x):
		lst = []
		for i in range(1, int(sqrt(x) + 1)):
			if x % i == 0:
				lst.append(i)
				if x != i ** 2:
					lst.append(x / i)
		return sum([k ** 2 for k in lst])
	return [[j, factors(j)] for j in range(m, n + 1) if sqrt(factors(j)) % 1 == 0]


from math import sqrt, pow

def list_divisors(n):
	s = set()
	i = 1
	while i <= sqrt(n):
		if i in s:
			continue
		(div, mod) = divmod(n, i)
		if mod == 0:
			s.add(i)
			if div != i:
				s.add(div)
		i = i + 1
	return sorted(list(s))

def list_squared(m, n):
	result = []
	for i in range(m, n + 1):
		divs_sum = sum((pow(d, 2) for d in list_divisors(i)))
		if sqrt(divs_sum).is_integer():
			result.append([i, divs_sum])
	return result


def divisors(n):
	divs = []
	for x in range(1, int(n ** 0.5) + 1):
		if n % x == 0:
			divs.extend([x ** 2, (n // x) ** 2])
	return sum(set(divs))

def list_squared(start, stop):
	squares = []
	for x in range(start, stop + 1):
		x_sum = divisors(x)
		if int(x_sum ** 0.5) ** 2 == x_sum:
			squares.append([x, x_sum])
	return squares


from math import sqrt
from functools import reduce
CACHE = {}

def get_divisors_gen(number):
	if number in CACHE:
		return CACHE[number]
	divisors = []
	for i in range(1, int(number / 2) + 1):
		if number % i == 0:
			divisors.append(i)
	divisors.append(number)
	CACHE[number] = divisors
	return divisors

def list_squared(m, n):
	result = []
	for number in range(m, n + 1):
		div_sq_sum = reduce(lambda acc, item: acc + item ** 2, get_divisors_gen(number))
		if sqrt(div_sq_sum).is_integer():
			result.append([number, div_sq_sum])
	return result


from functools import reduce

def factors(n):
	return set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))

def list_squared(m, n):
	ans = []
	for i in range(m, n):
		factor_sum = 0
		factor_ans = []
		for j in factors(i):
			factor_sum += j ** 2
		if (factor_sum ** 0.5).is_integer():
			factor_ans.append(i)
			factor_ans.append(factor_sum)
			ans.append(factor_ans)
	return ans


def list_squared(m, n):
	import numpy as np

	def find_divisor_square(n):
		arr = np.arange(1, n + 1)
		arr = n / arr
		divs = arr[arr == arr.astype(int)]
		return divs ** 2
	res = []
	for num in range(m, n):
		divs = find_divisor_square(num)
		sum_squres = divs.sum()
		if (sum_squres ** 0.5).is_integer():
			res.append([num, sum_squres])
	return res


import math

def list_squared(m, n):
	result = []
	for number in range(m, n):
		divisors = []
		for div in range(1, int(math.sqrt(number) + 1)):
			if number % div == 0:
				divisors.append(div)
		upper_divisors = [int(number / i) for i in divisors if i * i != number]
		divisors.extend(upper_divisors[::-1])
		div_sum = sum([i ** 2 for i in divisors])
		if math.sqrt(div_sum).is_integer():
			result.append([number, div_sum])
	return result


def list_squared(m, n):
	squared_divisors = []
	for i in range(m, n + 1):
		if i == 1:
			div = [1]
		else:
			div = [j for j in range(1, int(i ** 0.5) + 1) if i % j == 0 for j in (j, i // j) if i / j != j]
		tot = sum((k * k for k in div)) ** 0.5
		if tot == int(tot):
			squared_divisors.append([i, int(tot ** 2)])
	return squared_divisors


from math import sqrt

def list_squared(m, n):
	squares = []
	for i in range(m, n):
		i_squares = 0
		for j in range(1, int(sqrt(i) // 1) + 1):
			if i % j == 0:
				i_squares += j ** 2
				if i // j != j:
					i_squares += (i // j) ** 2
		if i_squares % sqrt(i_squares) == 0 and i_squares / sqrt(i_squares) == sqrt(i_squares):
			squares.append([i, i_squares])
	return squares


from functools import reduce

def factors(n):
	return set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))

def list_squared(m, n):
	result = []
	for i in range(m, n + 1):
		factors_sq = [x ** 2 for x in factors(i)]
		sum_factors = sum(factors_sq)
		sum_factors_root = sum_factors ** 0.5
		if sum_factors_root == int(sum_factors_root):
			result.append([i, sum_factors])
	return result


cache = {}

def sum_cache(n):
	if n not in cache:
		divs = [i for i in range(1, n + 1) if n % i == 0]
		cache[n] = sum([x * x for x in divs])
		return cache[n]
	return cache[n]

def list_squared(m, n):
	result = []
	for j in range(m, n + 1):
		summ = sum_cache(j)
		if (summ ** 0.5).is_integer():
			result.append([j, summ])
	return result


import math

def get_factors(m, n):
	cache = dict()
	for i in range(m, n + 1):
		factors = (j for j in range(1, 1 + i) if i % j == 0)
		total_sum = sum((j * j for j in factors))
		if math.sqrt(total_sum) % 1 == 0.0:
			cache[i] = total_sum
	return cache
FACTORS = get_factors(1, 10000)

def list_squared(m, n):
	return [[i, FACTORS[i]] for i in range(m, n + 1) if i in FACTORS]


def list_squared(m, n):
	answer = []
	for i in range(m, n + 1):
		root = sumSquares(factors(i)) ** 0.5
		if root == round(root):
			answer.append([i, int(root ** 2)])
	return answer
from functools import reduce

def factors(n):
	return set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n ** 0.5) + 1) if n % i == 0)))

def sumSquares(l):
	return sum((i ** 2 for i in l))