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A027760
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Denominator of Sum_{p prime, p-1 divides n} 1/p.
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33
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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
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OFFSET
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1,1
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COMMENTS
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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
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
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LINKS
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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.
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FORMULA
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EXAMPLE
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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, ...
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MAPLE
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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
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MATHEMATICA
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clausen[n_] := Product[i, {i, Select[ Map[ # + 1 &, Divisors[n]], PrimeQ]}]
f[n_] := Times @@ Select[Divisors@n + 1, PrimeQ]; Array[f, 56] (* Robert G. Wilson v, Apr 25 2012 *)
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PROG
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(Sage)
return mul(filter(lambda s: is_prime(s), map(lambda i: i+1, divisors(n))))
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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