Project Euler 3 Mystery Cache

Acknowledgements

This cache was inspired by Project Euler.

General notes

• To solve Project Euler puzzles, you will probably have to write a computer program.
• Many of the containers are small, and contain neither pen nor pencil.
• There are explicit finding notes in each geochecker.

The puzzle

The prime factors of 13195 are 5, 7, 13, and 29. Each occurs exactly once in the factorization.

Define f(n) as the largest prime factor of n, and g(n) as the sum of all of the prime factors.

For example,

100 = 2 ⨉ 2 ⨉ 5 ⨉ 5,

and so,

f(100) = 5,
g(100) = 2 + 2 + 5 + 5 = 14.

To find this cache, calculate:

• g(67108864)
• g(36)
• f(475262344414189)
• 0
• g(16)
• g(17592567)