# 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 \( 2 + 2 + 3 = 7 \).