login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027760 Denominator of Sum_{p prime, p-1 divides n} 1/p. 26
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, 2, 354, 2, 56786730, 2, 6, 2, 510, 2 (list; graph; refs; listen; history; text; 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). - 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. - Peter Luschny, Apr 29 2009

For N > 1, a(n) is the greatest number k such that x*y^n ==y*x^n (mod k) for any integers x and y.  Example: a(19) = 798 because x*y^19 ==y*x^19 (mod 798). - Michel Lagneau, Apr 21 2012

For n > 1, a(n) is the greatest number dividing numbers of the form k^n - k for every integer k. - Mateusz Szymański, Feb 18 2016

When n is even, a(n) is the product of the distinct primes dividing the denominator of zeta(1-n), where zeta(s) is the Riemann zeta function. - Griffin N. Macris, Jun 13 2016

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Thomas Clausen, Lehrsatz aus einer Abhandlung Über die Bernoullischen Zahlen, Astr. Nachr. 17 (1840), 351-352. [Peter Luschny, 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. [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.

Wikipedia, Bernoulli number

FORMULA

a(2*k) = A091137(2*k)/A091137(2*k-1). - Paul Curtz, Aug 05 2008

a(n) = product_{p prime, p-1 divides n}. - Eric M. Schmidt, Aug 01 2013

EXAMPLE

1/2, 5/6, 1/2, 31/30, 1/2, 41/42, 1/2, 31/30, 1/2, 61/66, 1/2, 3421/2730, 1/2, 5/6, 1/2, 557/510, ...

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: # R. J. Mathar, Aug 12 2008

MATHEMATICA

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

Table[clausen[i], {i, 1, 20}] (* Peter Luschny, Apr 29 2009 *)

f[n_] := Times @@ Select[Divisors@n + 1, PrimeQ]; Array[f, 56] (* Robert G. Wilson v, Apr 25 2012 *)

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

(Sage)

def A027760(n):

    return mul(filter(lambda s: is_prime(s), map(lambda i: i+1, divisors(n))))

[A027760(n) for n in (1..56)]  # Peter Luschny, May 23 2013

CROSSREFS

Cf. A027759, A027642, A141056.

Sequence in context: A076743 A131980 A217448 * A141056 A141498 A225481

Adjacent sequences:  A027757 A027758 A027759 * A027761 A027762 A027763

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

Formula submitted with A141417 added by R. J. Mathar, Nov 17 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 2 13:12 EST 2016. Contains 278678 sequences.