How to use if-function for arithmetic properties properly?

Hello everyone,

Im working on a project about the Ramanujans qth summation containing elements of signal processing. I try to simulate the entire formula via matlab yet Im not capable of finishing the if function with all the 3 properties (see picture) of the arithmetic theorem. This is my best attempt....

q = 12

primesfactorization = factor((q))

numbers=hist(primesfactorization, unique(primesfactorization));

m1 = numbers(1,1);

m2 = numbers(1,2);

p1=(primesfactorization(1,1)^m)

p2=primesfactorization(1,3)

XX Something is missing here, asking if p1 is a prime number then

if (q1)== mrdivide(q1,k)

q1 = q1-1

else(q1)~= mrdivide(q1,k)

q1 = -1

end

or p1= p^m for p is a prime and m<1 then

.....

Answer 1

[David Hill]

If you are trying to comute the ramanujan sum it should be something like this:

function s = ramanujanSum(a,n)
f=factor(a);
s=1;
for k=unique(f)
    b=nnz(f==k);
    if b==1
       if mod(n,k)==0
           s=s*(k-1);
       else
           s=-s;
       end
    elseif gcd(k^(b-1),n)==1
        s=0;
        return;
    elseif gcd(k^b,n)==1
        s=s*(-k^(b-1));
    else
        s=s*k^(b-1)*(k-1);
    end
end

[David Hill]

My code is generating the qth sum at n.

function c = ramanujanSum(q,n)
f=factor(q);
c=1;
for k=unique(f)
    b=nnz(f==k);%exponent of prime factor
    if b==1
       if mod(n,k)==0
           c=c*(k-1);
       else
           c=-c;
       end
    elseif gcd(k^(b-1),n)==1
        c=0;
        return;
    elseif gcd(k^b,n)==1
        c=c*(-k^(b-1));
    else
        c=c*k^(b-1)*(k-1);
    end
end