4
$\begingroup$

Starting with a positive integer $x$, find the sum of the $n^{th}$ powers of the prime factors of $x$, including multiplicities. Then find the sum of the $n^{th}$ prime factors of the result etc. until an $n^{th}$ power of a prime is reached. Will the sequence always terminate, or can it get caught in a loop or diverge to infinity?

python code for creating this sequence:

def factor(n):     m,p,r,k=n,3,7,[]     while m%2==0:         k.append(2)         r=1         m=m/2     while p<=n**0.5 and m!=1:         if m%p==0:             k.append(p)             r=1             m=m/p         else:             p+=2     if r==1:         while p<=n and m!=1:             if m%p==0:                 k.append(p)                 m=m/p             else:                 p+=2     return k y=1 x,n=int(input("start")),int(input("power")) while x!=y and x!=0:     y,x=x,0     t=factor(y)     for e in t:         x+=e**n     print(x) 
  • 1
    Your code doesn't seem to match the question. In the program it excludes primes that appear with multiplicity>1, i.e. unless `t.count(e)==1`. For example, with start=198 and power=2 it goes to $2^2+11^2=125$ and terminates, whereas from the question statement I would expect the next step to be $2^2+3^2+3^2+11^2=143$.2012-06-02

0 Answers 0