On a Mac Air it can only compute up to F(107) in a minute. It uses a "generator" concept to generate the number of possible premutations for each "generator" and sum them up.

an-algorithm-for-problem-454.py

from math import *

def euclid(a,b):
    #Euclidean algorithm 
    #compute the greatest common denominator
    if (b == 0):
      return a
    else:
      return euclid(b, a % b)

def F(L):
    m = 0
    x = 2
    maxX= int(sqrt(L))
    collection = 0
    while not(x>maxX):
        a = 1
        while(a<x):
            y = x+a
            if a==1 or euclid(x,y)==1:
                if not(x*y>L):
                    generated = int(L/(x*y))
                    #b = 1;
                    # while not(b>generated):
                    #   print x*b, y*b, x*y*b
                    #   b+= 1
                    collection += generated
                    #print x, y, x*y, ' generator generated ',generated,'permutation(s)'
            a+=1
        x+=1
    return collection