The function sigma 1, σ1 in mathematics, is known as the one that gives the sum of the divisors of an integer number.
For example for the number 10,
```python
σ1(10) = 18 # because the divisors of 10 are: 1, 2, 5, 10
σ1(10) = 1 + 2 + 5 + 10 = 18
```
You can see the graph of this important function up to 250:
The number 528 and its reversed, 825 have equal value for the function σ1.
```python
σ1(528) = σ1(825)
divisors of 528 are: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264 and 528
the sum of the divisors of 528 is 1488
divisors of 825 are: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275 and 825
the sum of the divisors of 825 is 1488
```
In fact 528 is the smallest non palindromic integer that has this property.
We need a function, ```equal_sigma1()```, that may collect all the positive integers that fulfill the property described above.
The function receives an upper limit, ```nMax```, will output the total sum of these numbers and its reversed while are less or equal nMax.
Let's see some cases:
```python
equal_sigma1(100) = 0 # There are no numbers.
equal_sigma1(1000) = 1353 # 528 and its revesed 825 were found, 528 +  825 = 1353
equal_sigma1(2000) = 4565 # There are four numbers_: 528 + 825 + 1561 + 1651 = 4565
equal_sigma1(1600) = 2914 # Now we have three numbers: 528 + 825 + 1561 = 2914
equal_sigma1(1561) = 2914
```
The palindromic numbers (like 88, 808, 929), numbers that are equal to its reversed should be discarded.
Happy coding!!
(For more information about the general sigma function see at: https://en.wikipedia.org/wiki/Divisor_function)
def sigma1(n):
    ans = 0
    for i in xrange(1,int(n**0.5) + 1):
        if n % i == 0:
            ans += i + n / i
    return ans if n ** 0.5 % 1 != 0 else ans - int(n ** 0.5)

def equal_sigma1(n_max):
    ans = 0
    for i in xrange(528,n_max+1):
        j = int(str(i)[::-1])
        if i != j and sigma1(i) == sigma1(j):ans += i
    return ans
def sigma1(n):
    ans = 0
    for i in xrange(1,int(n**0.5) + 1):
        if n % i == 0:
            ans += i + n / i
    return ans if n ** 0.5 % 1 != 0 else ans - int(n ** 0.5)

def equal_sigma1(n_max):
    ans = 0
    for i in xrange(528,n_max+1):
        j = int(str(i)[::-1])
        if i != j and sigma1(i) == sigma1(j):ans += i
    return ans