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

1, 2, 6, 2, 30, 6, 42, 2, 30, 10, 66, 6, 2730, 14, 30, 2, 510, 6, 798, 10, 2310, 22, 138, 6, 2730, 26, 6, 14, 870, 30, 14322, 2, 5610, 34, 210, 6, 1919190, 38, 78, 10, 13530, 42, 1806, 22, 690, 46, 282, 6, 46410, 10, 1122, 26, 1590, 6, 43890, 14, 16530, 58

Offset: 0

Author

Peter Luschny, May 29 2013

Keywords

• nonn

Comments

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).

Examples

			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'.
		

Links

• Peter Luschny, Table of n, a(n) for n = 0..100
• Peter Luschny, Generalized Bernoulli numbers.

Crossrefs

A027760, A160014, A226040.

Cf. A000040.

Programs

Haskell

a225481 n = product [p | p <- takeWhile (<= n + 1) a000040_list,
                         mod n (p - 1) == 0 || mod (n + 1) p == 0]
-- Reinhard Zumkeller, Jun 10 2013

Maple

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

Mathematica

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 *)

Sage

def divides(a, b): return b % a == 0
def A225481(n):
    return mul(filter(lambda p: divides(p,n+1) or divides(p-1,n), primes(n+2)))
[A225481(n) for n in (0..57)]

Formula

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