# Sum of a series

Algebra Level 2

You are told that

$$1 + 2 + 3 + \ldots + (n - 1) + n + (n - 1) + \ldots + 3 + 2 + 1 = 419,904$$

Work out the sum of $$n$$'s prime factors with multiplicity.

Hint - The prime factors of a number are the prime number(s) which when multiplied together make the original number. If the value of $$n$$ is 12, then $$12 = 2 \times 2 \times 3$$, and the sum will be $$2 + 2 + 3 = 7$$.

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