What is the sum of all distinct prime factors of 3^3 + 4^7 + 5^5 + 6^4 + 7^6

Question

The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 can be arranged into an addition sum to add up to almost any total, except that nobody has yet found a way to add up to 1984.
However 9 digits can equal 1984 by an addition sum.
Which digit is omitted?

Answer 1

3^3 + 4^7 + 5^5 + 6^4 + 7^6=138481
All Factors of 138481:
1, 7, 73, 271, 511, 1897, 19783, 138481
The Prime Factors are:
7 x 73 x 271
Sum of Prime Factors:
7+73+271=351