Number of Divisors Calculator

            def divisor_count(n: int) -> int:
    remaining, count, p = n, 1, 2
    while p * p <= remaining:
        exponent = 0
        while remaining % p == 0: remaining //= p; exponent += 1
        if exponent: count *= exponent + 1
        p = 3 if p == 2 else p + 2
    return count * (2 if remaining > 1 else 1)
assert divisor_count(12) == 6
          

            #include <assert.h>
#include <stdint.h>
uint64_t divisor_count(uint64_t n){uint64_t count=1;for(uint64_t p=2;p<=n/p;p+=(p==2?1:2)){unsigned e=0;while(n%p==0){n/=p;e++;}if(e)count*=e+1;}if(n>1)count*=2;return count;}
int main(void){assert(divisor_count(12)==6);}
          

            #include <cassert>
#include <cstdint>
std::uint64_t divisor_count(std::uint64_t n){std::uint64_t count=1;for(std::uint64_t p=2;p<=n/p;p+=(p==2?1:2)){unsigned e=0;while(n%p==0){n/=p;++e;}if(e)count*=e+1;}if(n>1)count*=2;return count;}
int main(){assert(divisor_count(12)==6);}
          

x86-64 NASM · System V ABI · Linux · integer arguments in rdi, rsi and rdx

            ; uint64_t divisor_count(uint64_t n)
global divisor_count
section .text
divisor_count:
    mov r8, 1
    mov rcx, 2
.factor:
    mov rax, rcx
    imul rax, rcx
    cmp rax, rdi
    ja .remaining
    xor r9d, r9d
.divide:
    mov rax, rdi
    xor edx, edx
    div rcx
    test rdx, rdx
    jnz .next
    mov rdi, rax
    inc r9
    jmp .divide
.next:
    test r9, r9
    jz .advance
    inc r9
    imul r8, r9
.advance:
    cmp rcx, 2
    jne .odd
    mov rcx, 3
    jmp .factor
.odd:
    add rcx, 2
    jmp .factor
.remaining:
    cmp rdi, 1
    jbe .done
    shl r8, 1
.done:
    mov rax, r8
    ret
          

            function result = divisor_count(n)
    n = abs(round(n)); result = 0;
    for k = 1:floor(sqrt(n))
        if mod(n, k) == 0, result = result + 1 + double(k ~= n / k); end
    end
end
          

            ClearAll[mwCalculate];
mwCalculate[n_Integer?Positive] := DivisorSigma[0, n];