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.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import numpy as np\n\n            \ndef binary_check(x):\n    if x == 1: return True\n    start = 0\n    stop = x//2\n    sol = []\n    while start <= stop:\n        mid = (start+stop) // 2\n        \n        if mid*mid == x:\n            return True\n        if mid*mid < x:\n            start = mid + 1\n        if mid*mid > x:\n            stop = mid - 1\n\nimport collections\nimport itertools\n\n\ndef prime_factors(n):\n    i = 2\n    while i * i <= n:\n        if n % i == 0:\n            n /= i\n            yield i\n        else:\n            i += 1\n\n    if n > 1:\n        yield n\n\n\ndef prod(iterable):\n    result = 1\n    for i in iterable:\n        result *= i\n    return result\n\n\ndef get_divisors(n):\n    pf = prime_factors(n)\n\n    pf_with_multiplicity = collections.Counter(pf)\n\n    powers = [\n        [factor ** i for i in range(count + 1)]\n        for factor, count in list(pf_with_multiplicity.items())\n    ]\n\n    for prime_power_combo in itertools.product(*powers):\n        yield prod(prime_power_combo)\n            \ndef list_squared(m, n):\n    sol = []\n    \n    for number in range(m,n):\n        candidate = [i**2 for i in range(1,number+2) if number % i == 0]\n        n = sum(candidate)\n        if binary_check(n):\n            sol.append([number,n])\n    return sol\n\n\ndef list_squared(m, n):\n    sol = []\n    for number in range(m,n):\n        candidate = [i*i for i in get_divisors(number)]\n        n=int(sum(candidate))\n        if binary_check(n):\n            sol.append([number,n])\n    return sol\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'list_squared'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 19913