create vectors using exponent/power for numbers using prime powers - matlab

Question

I am trying to create vectors for every number up to n by just using the exponents of the prime numbers, using prime vector PV=[2 3 5 7 11 13 17 19 23 29] to recognize each number and store these vectors for later calculations. My PVE=[k k k k k k k k k k x], with k being the exponents corrisponding to PV, and x is the exponent of any prime that PV does not divide, so x will always be 0 or 1 because my n is 960=(31^2)-1. So if any number in this set divides some number 9, for instance the vector exponent of 9 would be [0 2 0 0 0 0 0 0 0 0 0] as 3^2 is 9. and the vector for 22 would be [1 0 0 0 1 0 0 0 0 0 0] and this is 2*11=22. so every "numba" as in my program from 2 to n would have a prime vector exponent (PVE). This comes from the fundamental theorem of arithmetic that every number can be expressed as the product of primes, and it is unique.
Could you please look at my program to see what I am doing wrong to get the exponents.
Program:
n=960
for numba=2:n
for c=2:numba-1
if numba==2
c=2
if mod(numba,c)~=0
numba=p
end
end
end
end
for k=1:9
PVEC=[2^k 3^k 5^k 7^k 11^k 13^k 17^k 19^k 23^k 29^k]
if p>29
if mod(numba,PVEC)==0
max(PVEC,k) & PVE==[k k k k k k k k k k 0]
if mod(numba,PVE)~=0
PVE=[0 0 0 0 0 0 0 0 0 0 1]
end
end
end
end

Answer 1

You can compute PVE for each numba in one line, using factors and histc:
PVE = histc(factor(numba),[PV inf])
Example:
>> PV = [2 3 5 7 11 13 17 19 23 29];
>> numba = 22;
>> PVE = histc(factor(numba),[PV inf])
PVE =
1 0 0 0 1 0 0 0 0 0 0
>> numba = 9;
>> PVE = histc(factor(numba),[PV inf])
PVE =
0 2 0 0 0 0 0 0 0 0 0

Answer 2

I don't quite understand what you are trying to do in your first loop, but if I were you, I would use recursion to get an exponent. Something like this...
function [ expo ] = get_exponent( p, num, depth )
% return the exponent
% p: prime number
% num: number to be analyzed
% depth: depth of the recursion
if p==1,
error ('Do not use 1 for p!!')
end
if mod(num,p) == 0,
depth = depth+1;
expo = get_exponent(p, num/p, depth);
else
expo = depth;
end
end
This get_exponent function returns the exponent for some number num of some prime p. For example,
>> get_exponent(5,325,0)
ans =
2
>> get_exponent(13,325,0)
ans =
1
Use this function in your second loop to get exponent of each prime.