Return the nth digit of the sequence of aliquot series 0. DEFINITIONS

A sequence is a list of numbers.
A series is the sum of a list of numbers.
The set of natural numbers contains all "non-negative integers greater than zero". 
A divisor (in this context) of a natural number j is a natural number i, such that j&div;i is also a natural number.

1. PREAMBLE

A couple of other questions on this site mention the concept of the aliquot, or the sequence of divisors of a natural number a which are less than a. Determining amicable numbers involves computing the sum of these divisors, called an aliquot sum or aliquot series. Every natural number has its own aliquot sum, although the value of a number's aliquot sum is not necessarily unique to that number. (Exempli gratia, every prime number has an aliquot sum of 1.)

2. CHALLENGE

Given a natural number n, return the nth digit of the sequence of aliquot sums. The first several series in the sequence, starting with the series for 1, are:

{0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 11, 14, 1, 36, 6, 16, 13}


Concatenated, these look like:

0113161748116110915121122111413661613


Input may be zero-indexed or one-indexed, according to your preference. Solutions must be programs or functions capable of returning the 10,000th digit (input up to 9999 or 10000). The shortest working solution wins.

3. TEST CASES

Correct input-output pairs should include, but are not limited to, the following:

   0 or     1    -&gt;    0
   4 or     5    -&gt;    1
  12 or    13    -&gt;    6
9999 or 10000    -&gt;    7


The number preceding the "or" is 0-indexed; the number following is 1-indexed.
Additional test cases may be provided upon request.

4. REFERENCES

OEIS has a list of numbers and their aliquot sums.
Mathematica, 51 bytes

Array[##&amp;@@IntegerDigits[Tr@Divisors@#-#]&amp;,#][[#]]&amp;


An unnamed function which takes and returns an integer and uses 1-based indexing. Handles input 10000 instantly.

Explanation

This is a very straight-forward implementation of the definition, making use of the fact that the first n divisor sums are always enough to determine the nth digit. As usual, the reading order of golfed Mathematica is a bit funny though:

Array[...&amp;,#]...&amp;


This generates a list with all the results of applying the unnamed function on the left to all the values i from 1 to n inclusive.

...Tr@Divisors@#-#...


We start by computing the divisors of i, summing them with Tr and subtracting i itself so that it's just the sum of divisors less than i.

...IntegerDigits[...]...


This turns the result into a list of its decimal digits.

##&amp;@@...


And this removes the "list" head, so that all the digit lists are automatically concatenated in the result of Array. For more details on how ## works, see the "Sequences of arguments" section in this post.

...[[#]]


Finally, we select the nth digit from the result.