A226038 -id:A226038 - cp's OEIS frontend

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

Peter Luschny, May 26 2013

nonn

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

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

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

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);

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 *)

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

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)]

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

A226039 Numbers k such that there exist primes p which divide k+1 and p-1 does not divide k.

Original entry on oeis.org

5, 9, 11, 13, 14, 17, 19, 20, 21, 23, 25, 27, 29, 32, 33, 34, 35, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 101, 103

Offset: 1

Peter Luschny, May 27 2013

nonn

			20 is in this list because 7 divides 21 but 6 does not divide 20.

Peter Luschny, Generalized Bernoulli numbers.

Cf. A226038, A226040.

s := (p,n) -> ((n+1) mod p = 0) and (n mod (p-1) <> 0);
F := n -> select(p -> s(p,n), select('isprime', [$2..n]));
A226039_list := n -> select(k -> [] <> F(k), [$0..n]);
A226039_list(103);

selQ[n_] := AnyTrue[Prime[Range[PrimePi[n+1]]], Divisible[n+1, #] && !Divisible[n, #-1]&];
Select[Range[103], selQ] (* Jean-François Alcover, Jul 08 2019 *)

def F(n): return any(p for p in primes(n) if (n+1) % p == 0 and n % (p-1) != 0)
def A226039_list(n): return list(filter(F, (0..n)))
A226039_list(103)

cp's OEIS Frontend

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

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