2016-03-03 Exam, doubts and poetry

This is one question we decided to remove from the final exam but I still do like it because it challenges people. How to make a connection between known algorithms and the following code. To your opinion, the following code is closed to:

import math

def meslogs_jusque(N):
    memolog = { 1:0.0 }
    for i in range(2,N+1):
        if i in memolog:
            pass
        else:
            l = math.log(i)
            total = i
            for j in range(total, N+1, total):
                memolog[j] = memolog.get(j, 0.0) + l
            total *= i
            while total < N+1:
                for j in range(total, N+1, total):
                    memolog[j] += l
                total *= i
    return memolog