Search: id:A027760
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%I A027760
%S A027760 2,6,2,30,2,42,2,30,2,66,2,2730,2,6,2,510,2,798,2,330,2,
%T A027760 138,2,2730,2,6,2,870,2,14322,2,510,2,6,2,1919190,2,6,2,
%U A027760 13530,2,1806,2,690,2,282,2,46410,2,66,2,1590,2,798,2,870
%N A027760 Denominator of Sum 1/p; p-1 | n.
%C A027760 The gcd of integers x^(n+1)-x, for all integers x. - Roger Cuculiere 
               (cuculier(AT)imaginet.fr), Jan 19 2002
%C A027760 If each x in a ring satisfies x^(n+1)=x, the characteristic of the ring 
               is a divisor of a(n) (Rosenblum 1977). [From Daniel M. Rosenblum 
               (DMRosenblum(AT)world.oberlin.edu), Sep 24 2008]
%C A027760 A formula in A091137 suggests that this is the same as A140770. [From 
               R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 23 2009]
%C A027760 The denominators of the Bernoulli numbers for n>0. B_n sequence begins 
               1, -1/2, 1/6, 0/2, -1/30, 0/2, 1/42, 0/2, ... This is an alternative 
               version of A027642 suggested by the theorem of Clausen. To add a(0) 
               = 1 has been proposed in A141056. [From Peter Luschny (peter(AT)luschny.de), 
               Apr 29 2009]
%D A027760 S. C. Locke and A. Mandel, Problem E 2901, American Mathematical Monthly 
               88 (1981), p. 538. Solution in Vol. 90 (1983), pp. 212-213. [From 
               Daniel M. Rosenblum (DMRosenblum(AT)world.oberlin.edu), Jul 31 2008]
%D A027760 D. M. Rosenblum, Problem 1019, Mathematics Magazine 50 (1977), p. 164. 
               Solution by T. Orloff in Vol. 52 (1979), p. 50.
%D A027760 Clausen, Thomas, "Lehrsatz aus einer Abhandlung Ueber die Bernoullischen 
               Zahlen", Astr. Nachr. 17 (1840), 351-352. [From Peter Luschny (peter(AT)luschny.de), 
               Apr 29 2009]
%H A027760 Wikipedia, <a href="http://en.wikipedia.org/wiki/Bernoulli_number">Bernoulli 
               number</a> [From Peter Luschny (peter(AT)luschny.de), Apr 29 2009]
%p A027760 A027760 := proc(n) local s,p; s := 0 ; p := 2; while p <= n+1 do if n 
               mod (p-1) = 0 then s := s+1/p; fi; p := nextprime(p) ; od: denom(s) 
               ; end: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 12 
               2008]
%t A027760 Contribution from Peter Luschny (peter(AT)luschny.de), Apr 29 2009: (Start)
%t A027760 clausen[n_] := Product[i, {i, Select[ Map[ # + 1 &, Divisors[n]], PrimeQ]}]
%t A027760 Table[clausen[i], {i, 1, 20}] (End)
%Y A027760 Cf. A027759.
%Y A027760 Cf. A027642, A141056. [From Peter Luschny (peter(AT)luschny.de), Apr 
               29 2009]
%Y A027760 Sequence in context: A131980 A076743 A141056 this_sequence A140770 A141498 
               A144845
%Y A027760 Adjacent sequences: A027757 A027758 A027759 this_sequence A027761 A027762 
               A027763
%K A027760 nonn,frac
%O A027760 1,1
%A A027760 N. J. A. Sloane (njas(AT)research.att.com).

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