Do Bernoulli Numbers Always Have Unique Prime Factors in Their Denominators?

[Damidami]

Is this a known bernoulli number conjeture/theorem?:
The denominators of B_n (when expressed as an irreducible fraction), doesn't contain as a factor powers of prime numbers (ex. isn't divided by 5^2)

Example:

B_2 = 1/6
6 = 2*3

B_4 = -1/30
30 = 2*3*5

B_{24} = -236364091/2730
2730 = 2*3*5*7*13

I know Ramanujan proved that the denominator contain 2 and 3 as a factor one and only once, but I hadn't heard that any prime on the factorization of the denominator happens only once.

 

[Damidami]

Nevermind.

http://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem"

Aditional information is welcome.