%I #14 Jun 10 2013 17:33:09

%S 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 2730,26,6,14,870,30,14322,2,5610,34,210,6,1919190,38,78,10,13530,42,

%U 1806,22,690,46,282,6,46410,10,1122,26,1590,6,43890,14,16530,58

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

%C 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 Peter Luschny, <a href="/A225481/b225481.txt">Table of n, a(n) for n = 0..100</a>

%H Peter Luschny, <a href="http://www.luschny.de/math/euler/GeneralizedBernoulliNumbers.html">Generalized Bernoulli numbers</a>.

%F a(n) / A027760(n) = A226040(n) for n > 0.

%e 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 divides := (a, b) -> b mod a = 0; primes := n -> select(isprime, [$2..n]);

%p 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 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 (Sage)

%o def divides(a, b): return b % a == 0

%o def A225481(n):

%o return mul(filter(lambda p: divides(p,n+1) or divides(p-1,n), primes(n+2)))

%o [A225481(n) for n in (0..57)]

%o (Haskell)

%o a225481 n = product [p | p <- takeWhile (<= n + 1) a000040_list,

%o mod n (p - 1) == 0 || mod (n + 1) p == 0]

%o -- _Reinhard Zumkeller_, Jun 10 2013

%Y A027760, A160014, A226040.

%Y Cf. A000040.

%K nonn

%O 0,2

%A _Peter Luschny_, May 29 2013