p853 multiples generator

p853_multiples_generator.py

def gen_multiples(primes, pivalues, multiplicities, limit):
    #Generates all multiples of given primes up to a cetain multiplicity
    #Extra condition to precalculate pi(n)
    p, vpi = 1, 1
    multiples = []
    for i in range(multiplicities[0] + 1):
        if p > 1:
            multiples.append((p, vpi))
            
        if len(primes) > 1:
            for (x, xpi) in gen_multiples(primes[1:], pivalues[1:], multiplicities[1:], limit//p):
                if p*x < limit:
                    multiples.append((p*x, lcm(vpi, xpi)))
        
        if i == 0:
            p *= primes[0]
            vpi *= pivalues[0]
        else:
            p *= primes[0]
            vpi *= primes[0]
    return multiples