cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A006954 Denominators of Bernoulli numbers B_0, B_1, B_2, B_4, B_6, ...

Original entry on oeis.org

1, 2, 6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530, 1806, 690, 282, 46410, 66, 1590, 798, 870, 354, 56786730, 6, 510, 64722, 30, 4686, 140100870, 6, 30, 3318, 230010, 498, 3404310, 6, 61410, 272118, 1410, 6, 4501770
Offset: 0

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These are the denominators if you hurriedly look down a list of the nonzero Bernoulli numbers without noticing that B_1 has been included.
From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.

References

  • M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260.
  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.1, p. 41.
  • G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
  • H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Programs

  • Mathematica
    Join[{1,2},Denominator[BernoulliB[Range[2,100,2]]]] (* Harvey P. Dale, Apr 11 2016 *)

Formula

E.g.f: t/(e^t - 1).

Extensions

More terms from T. D. Noe, Mar 31 2004