A006954 Denominators of Bernoulli numbers B_0, B_1, B_2, B_4, B_6, ... (Formerly M1689 N0667)

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

0,2

Comments

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.

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).

Links

Table of n, a(n) for n=0..49.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260.

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Index entries for sequences related to Bernoulli numbers.

Formula

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

Mathematica

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

Crossrefs

Cf. A000367, A002445, A027762.

Sequence in context: A324887 A346106 A330326 * A360681 A286652 A265501

Adjacent sequences: A006951 A006952 A006953 * A006955 A006956 A006957

Keyword

nonn,frac

Author

N. J. A. Sloane, Simon Plouffe

Extensions

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

Status

approved