Damidami
Sep27-09, 12:49 PM
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.
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.