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Bernoulli Number's conjeture?

  1. Sep 27, 2009 #1
    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)


    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.
  2. jcsd
  3. Sep 27, 2009 #2

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

    Aditional information is welcome.
    Last edited by a moderator: May 4, 2017
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