MATLAB: How can i add a prime counting function to this

MATLABprimer counter sieve of eratosthenes

function [ p, c ] = sieve( N )
  % Sieve Of Erastothenes Test - [ p, c ] = sieve( 100 )
  % The Sieve of Erastothenes is an ancient algorithm for finding prime numbers.
  % For example, to find all prime numbers less than 100, list the whole numbers from 1 to 100, then
  % remove multiples of 2 , then multiples of 3, then multiples of the next prime number, 5, and so
  % on up to multiples of 7 (deleting multiples of prime numbers larger than 100 is unnecessary).
    %%Prime number sorter (p)
    p = ( 1 : 2 : N ); % Holds the prime numbers generated
                   % p = 1 3 5 7 9 ... N (Halves numbers required to find
                   % primes) ie, remove all even numbers but 2
    q = length(p); % Auto expand vector from N
    p(1) = 2;      % p = 2 3 5 7 9 ... N
                   % Optimised to find primes by factor not exceeding
                   % root N
            for i = 3 : 2 : sqrt(N)
                if p( (i + 1)/2 )
                   p( ( (i.^2 + 1)/2) : i : q ) = 0; 
                end 
            end
    p = p( p > 0 ); % Omit zeroes in final prime list
    %%Prime counting function (c)
    L = logical(p);
    c = cumsum(L);
    end
How would i go about adding a prime counter, i.e. ?(1) = 0, ?(2) = 1, ?(3) = 2, ?(4) = 2, ?(5) = 3 and so on. My issue is i have optimised the code by removing all even numbers but 2 and removing the zeroes at the end but for the counting function i require all the 1×100 numbers to convert into a logical array and add them cumulatively to generate the correct result. My arrays output at 1×25 with the zeroes and even numbers omitted.
My main idea was to add them back in just for the prime counter, but I have been unsuccessful so far.

Best Answer

n = zeros(1,N);
n(p) = 1;
c = cumsum(n);
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