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

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

Author

Peter Luschny, May 27 2013

Keywords

• nonn

Examples

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

Links

• Peter Luschny, Generalized Bernoulli numbers.

Crossrefs

Cf. A226038, A226040.

Programs

Maple

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);

Mathematica

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

Sage

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)