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%I M1689 N0667 #33 Nov 01 2024 02:07:09
%S 1,2,6,30,42,30,66,2730,6,510,798,330,138,2730,6,870,14322,510,6,
%T 1919190,6,13530,1806,690,282,46410,66,1590,798,870,354,56786730,6,
%U 510,64722,30,4686,140100870,6,30,3318,230010,498,3404310,6,61410,272118,1410,6,4501770
%N Denominators of Bernoulli numbers B_0, B_1, B_2, B_4, B_6, ...
%C These are the denominators if you hurriedly look down a list of the nonzero Bernoulli numbers without noticing that B_1 has been included.
%C From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260.
%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.1, p. 41.
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
%D H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 260.
%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>
%F E.g.f: t/(e^t - 1).
%t Join[{1,2},Denominator[BernoulliB[Range[2,100,2]]]] (* _Harvey P. Dale_, Apr 11 2016 *)
%Y Cf. A000367, A002445, A027762.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from _T. D. Noe_, Mar 31 2004