1,1

The gcd of integers x^(n+1)-x, for all integers x. - Roger Cuculiere (cuculier(AT)imaginet.fr), Jan 19 2002

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]

A formula in A091137 suggests that this is the same as A140770. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 23 2009]

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]

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. M. Rosenblum, Problem 1019, Mathematics Magazine 50 (1977), p. 164. Solution by T. Orloff in Vol. 52 (1979), p. 50.

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]

Wikipedia, Bernoulli number [From Peter Luschny (peter(AT)luschny.de), Apr 29 2009]

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]

Contribution from Peter Luschny (peter(AT)luschny.de), Apr 29 2009: (Start)

clausen[n_] := Product[i, {i, Select[ Map[ # + 1 &, Divisors[n]], PrimeQ]}]

Table[clausen[i], {i, 1, 20}] (End)

Cf. A027759.

Cf. A027642, A141056. [From Peter Luschny (peter(AT)luschny.de), Apr 29 2009]

Adjacent sequences: A027757 A027758 A027759 this_sequence A027761 A027762 A027763

Sequence in context: A131980 A076743 A141056 this_sequence A140770 A141498 A144845

nonn,frac

N. J. A. Sloane (njas(AT)research.att.com).