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A225481 a(n) = product{ p primes <= n+1 such that p divides n+1 or p-1 divides n }.

%I A225481 #14 Jun 10 2013 17:33:09
%S A225481 1,2,6,2,30,6,42,2,30,10,66,6,2730,14,30,2,510,6,798,10,2310,22,138,6,
%T A225481 2730,26,6,14,870,30,14322,2,5610,34,210,6,1919190,38,78,10,13530,42,
%U A225481 1806,22,690,46,282,6,46410,10,1122,26,1590,6,43890,14,16530,58
%N A225481 a(n) = product{ p primes <= n+1 such that p divides n+1 or p-1 divides n }.
%C A225481 a(n) is the product over the primes <= n+1 which satisfy the weak Clausen condition. The weak Clausen condition relaxes the Clausen condition (p-1)|n by logical disjunction with p|(n+1).
%H A225481 Peter Luschny, <a href="/A225481/b225481.txt">Table of n, a(n) for n = 0..100</a>
%H A225481 Peter Luschny, <a href="http://www.luschny.de/math/euler/GeneralizedBernoulliNumbers.html">Generalized Bernoulli numbers</a>.
%F A225481 a(n) / A027760(n) = A226040(n) for n > 0.
%e A225481 a(20) = 2310 = 2*3*5*7*11, because {3, 7} are divisors of 21 and {2, 5, 11} meet the Clausen condition 'p-1 divides n'.
%p A225481 divides := (a, b) -> b mod a = 0; primes := n -> select(isprime, [$2..n]);
%p A225481 A225481 := n -> mul(k,k in select(p -> divides(p,n+1) or divides(p-1,n), primes(n+1))); seq(A225481(n), n = 0..57);
%t A225481 a[n_] := Product[ If[ Divisible[n+1, p] || Divisible[n, p-1], p, 1], {p, Prime /@ Range @ PrimePi[n+1]}]; Table[a[n], {n, 0, 57}] (* _Jean-François Alcover_, Jun 07 2013 *)
%o A225481 (Sage)
%o A225481 def divides(a, b): return b % a == 0
%o A225481 def A225481(n):
%o A225481     return mul(filter(lambda p: divides(p,n+1) or divides(p-1,n), primes(n+2)))
%o A225481 [A225481(n) for n in (0..57)]
%o A225481 (Haskell)
%o A225481 a225481 n = product [p | p <- takeWhile (<= n + 1) a000040_list,
%o A225481                          mod n (p - 1) == 0 || mod (n + 1) p == 0]
%o A225481 -- _Reinhard Zumkeller_, Jun 10 2013
%Y A225481 A027760, A160014, A226040.
%Y A225481 Cf. A000040.
%K A225481 nonn
%O A225481 0,2
%A A225481 _Peter Luschny_, May 29 2013