Search: id:A002445
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%I A002445 M4189 N1746
%S A002445 1,6,30,42,30,66,2730,6,510,798,330,138,2730,6,870,14322,
%T A002445 510,6,1919190,6,13530,1806,690,282,46410,66,1590,798,870,
%U A002445 354,56786730,6,510,64722,30,4686,140100870,6,30,3318,230010
%N A002445 Denominators of Bernoulli numbers B_2n.
%C A002445 From the Von Staudt-Clausen theorem, denominator(B_2n) = product of primes 
               p such that (p-1)|2n.
%C A002445 Row products of A138239. - Mats Granvik (mgranvik(AT)abo.fi), Mar 08 
               2008
%C A002445 Equals row products of even rows in triangle A143343. In triangle A080092, 
               row products = denominators of B1, B2, B4, B6,... [From Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Aug 09 2008]
%C A002445 Julius Worpitzky's 1883 algorithm for generating Bernoulli numbers is 
               shown in A028246. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 
               09 2008]
%D A002445 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%D A002445 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002445 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002445 See A000367 for further references and links (there are a lot).
%H A002445 T. D. Noe, <a href="b002445.txt">Table of n, a(n) for n=0..10000</a>
%H A002445 G. Everest, A. J. van der Poorten, Y. Puri and T. Ward, <a href="http:/
               /www.cs.uwaterloo.ca/journals/JIS/index.html">Integer Sequences and 
               Periodic Points</a>, Journal of Integer Sequences, Vol. 5 (2002), 
               Article 02.2.3
%H A002445 Niels Nielsen, <a href="http://gallica.bnf.fr/scripts/ConsultationTout.exe?O=N062119">
               Traite Elementaire des Nombres de Bernoulli</a>, Gauthier-Villars, 
               1923, pp. 398.
%H A002445 S. Plouffe, <a href="http://www.ibiblio.org/gutenberg/etext01/brnll10.txt">
               The First 498 Bernoulli numbers</a> [Project Gutenberg Etext]
%H A002445 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%F A002445 E.g.f: t/(e^t - 1).
%F A002445 B_{2n}/(2n)! = 2*(-1)^(n-1)*(2*Pi)^(-2n) Sum_{k=1..inf} 1/k^(2n) (gives 
               asymptotics) - Rademacher, p. 16, Eq. (9.1). In particular, B_{2*n} 
               ~ (-1)^(n-1)*2*(2*n)!/(2*Pi)^(2*n).
%e A002445 B_{2n} = [ 1, 1/6, -1/30, 1/42, -1/30, 5/66, -691/2730, 7/6, -3617/510,
               ... ].
%o A002445 (PARI) a(n)=prod(p=2,2*n+1,if(isprime(p),if((2*n)%(p-1),1,p),1)) (Benoit 
               Cloitre)
%Y A002445 Cf. A090801 (distinct numbers appearing as denominators of Bernoulli 
               numbers)
%Y A002445 B_n gives A027641/A027642. See A027641 for full list of references, links, 
               formulae, etc.
%Y A002445 See A000367 for numerators. Cf. A027762, A027641, A027642.
%Y A002445 Cf. also A002882, A003245, A127187, A127188.
%Y A002445 Cf. A138239.
%Y A002445 Cf. A028246, A143343, A080092 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 09 2008]
%Y A002445 Sequence in context: A067879 A136375 A138706 this_sequence A027762 A151711 
               A130512
%Y A002445 Adjacent sequences: A002442 A002443 A002444 this_sequence A002446 A002447 
               A002448
%K A002445 nonn,frac,nice
%O A002445 0,2
%A A002445 N. J. A. Sloane (njas(AT)research.att.com).

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