Question

Let f(n) be the function that assigns to each integer greater than 1 the sum of its distinct prime factors. For example, since 2 and 5 are the only prime factors of 20, f(20)=7, and since 5 is the only prime factor of 25, f(25)=5. Which of the following statements are true?

f(2n)=f(n)
f(2n)=f(n)+2
f(2n)=2f(n)

Answer 1

for the first one let n=3.
for the second one let n=2.
for the third one let n = 15.

Answer 2

f(2n)=f(n)+2

Answer 3

i am new to os, are we allowed to give out answers

Answer 4

Right, so if n=2 then we have:

f(4)=f(2)+2

which evaluates to

2=2+2

So true or false?

Answer 5

f(ab) = f(a)+f(b)

whenever gcd(a,b)=1

Answer 6

so we may say

f(2n) = f(2) + f(n)

whenever n is odd

Answer 7

wait a second, i think i have interpreted the question incorrectly
it is about "adding the distinct prime factors", not just number of distinct primes

Answer 8

I think it shouldn't matter either way since both are logarithm alike !