OpenMP threads executing on the same cpu core

I'm currently parallelizing program using openmp on a 4-core phenom2. However I noticed that my parallelization does not do anything for the performance. Naturally I assumed I missed something (falsesharing, serialization through locks, ...), however I was unable to find anything like that. Furthermore from the CPU Utilization it seemed like the program was executed on only one core. From what I found sched_getcpu() should give me the Id of the core the thread executing the call is currently scheduled on. So I wrote the following test program:

#include <iostream>
#include <sstream>
#include <omp.h>
#include <utmpx.h>
#include <random>
int main(){
    #pragma omp parallel
    {
        std::default_random_engine rand;
        int num = 0;
    #pragma omp for
        for(size_t i = 0; i < 1000000000; ++i) num += rand();
    auto cpu = sched_getcpu();
    std::ostringstream os;
        os<<"\nThread "<<omp_get_thread_num()<<" on cpu "<<sched_getcpu()<<std::endl;
        std::cout<<os.str()<<std::flush;
    std::cout<<num;
    }
}

On my machine this gives the following output(the random numbers will vary of course):

Thread 2 on cpu 0 num 127392776
Thread 0 on cpu 0 num 1980891664
Thread 3 on cpu 0 num 431821313
Thread 1 on cpu 0 num -1976497224

From this I assume that all threads execute on the same core (the one with id 0). To be more certain I also tried the approach from this answer. The results where the same. Additionally using #pragma omp parallel num_threads(1) didn't make the execution slower (slightly faster in fact), lending credibility to the theory that all threads use the same cpu, however the fact that the cpu is always displayed as 0 makes me kind of suspicious. Additionally I checked GOMP_CPU_AFFINITY