|
| |
|
|
A027760
|
|
Denominator of Sum 1/p; p-1 | n.
|
|
20
| |
|
|
2, 6, 2, 30, 2, 42, 2, 30, 2, 66, 2, 2730, 2, 6, 2, 510, 2, 798, 2, 330, 2, 138, 2, 2730, 2, 6, 2, 870, 2, 14322, 2, 510, 2, 6, 2, 1919190, 2, 6, 2, 13530, 2, 1806, 2, 690, 2, 282, 2, 46410, 2, 66, 2, 1590, 2, 798, 2, 870
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| 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]
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]
|
|
|
REFERENCES
| 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]
|
|
|
LINKS
| Wikipedia, Bernoulli number [From Peter Luschny (peter(AT)luschny.de), Apr 29 2009]
|
|
|
FORMULA
| a(2*k) = A091137(2*k)/A091137(2*k-1). [Paul Curtz (bpcrtz(AT)free.fr), Aug 05 2008]
|
|
|
MAPLE
| 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]
|
|
|
MATHEMATICA
| 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)
|
|
|
PROG
| (PARI) a(n)=denominator(sumdiv(n, d, if(isprime(d+1), 1/(d+1)))) \\ Charles R Greathouse IV, Jul 08 2011
(PARI) a(n)=my(pr=1); fordiv(n, d, if(isprime(d+1), pr*=d+1)); pr \\ Charles R Greathouse IV, Jul 08 2011
|
|
|
CROSSREFS
| Cf. A027759.
Cf. A027642, A141056. [From Peter Luschny (peter(AT)luschny.de), Apr 29 2009]
Sequence in context: A125032 A131980 A076743 * A141056 A141498 A144845
Adjacent sequences: A027757 A027758 A027759 * A027761 A027762 A027763
|
|
|
KEYWORD
| nonn,frac
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Added formula submitted with A141417 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 17 2010
|
| |
|
|
