A226040 a(n) = product{ p prime such that p divides n + 1 and p - 1 does not divide n }.

1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 7, 5, 1, 1, 3, 1, 5, 7, 11, 1, 3, 1, 13, 1, 7, 1, 15, 1, 1, 11, 17, 35, 3, 1, 19, 13, 5, 1, 21, 1, 11, 1, 23, 1, 3, 1, 5, 17, 13, 1, 3, 55, 7, 19, 29, 1, 15, 1, 31, 7, 1, 13, 33, 1, 17, 23, 35, 1, 3, 1, 37, 5, 19, 77, 39

Offset: 0

Author

Peter Luschny, May 26 2013

Keywords

• nonn

Examples

			a(41) = 21 = 3*7 = product({2,3,7} setminus {2}).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
• Peter Luschny, Generalized Bernoulli numbers.

Crossrefs

Cf. A160014, A226038, A226039, A225481, A141056.

Programs

Maple

s:= (p, n) -> ((n+1) mod p = 0) and (n mod (p-1) <> 0);
A226040 := n -> mul(z, z = select(p->s(p,n), select('isprime', [$2..n])));
seq(A226040(n), n=0..77);

Mathematica

a[n_] := Times @@ Select[ FactorInteger[n+1][[All, 1]], !Divisible[n, #-1] &]; a[0] = 1; Table[a[n], {n, 0, 77}] (* Jean-François Alcover, Jun 27 2013, after Maple *)

PARI

a(n)=my(f=factor(n+1)[,1],s=1);prod(i=1,#f,if(n%(f[i]-1),f[i],1)) \\ Charles R Greathouse IV, Jun 27 2013

Sage

def A226040(n):
    F = filter(lambda p: ((n+1) % p == 0) and (n % (p-1)), primes(n))
    return mul(F)
[A226040(n) for n in (0..77)]

Formula

a(n) = A225481(n) / A141056(n).