Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.

```
n Relatively Prime φ(n) n/φ(n)
2 1 1 2
3 1,2 2 1.5
4 1,3 2 2
5 1,2,3,4 4 1.25
6 1,5 2 3
7 1,2,3,4,5,6 6 1.1666...
8 1,3,5,7 4 2
9 1,2,4,5,7,8 6 1.5
10 1,3,7,9 4 2.5
```

It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10.

Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

```
In [1]:
```from sympy import primerange
P = 1
for p in primerange(1, 100):
P *= p
if P > 1000000:
break
print(P//p)

```
```

**Explanation:** n/φ(n) is equal to the product of p/(p-1) for all distinct prime divisors of n.
We may assume that n has no repeated prime factors (i.e. is square free), because repeating a prime factor would increase the value of n without changing the value of n/φ(n). We may also assume that the prime factors are consecutive, because replacing one prime with a smaller prime would increase the product.
So the answer is the largest product of consecutive primes (starting at 2) that is less than 1,000,000.