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A226039
Numbers k such that there exist primes p which divide k+1 and p-1 does not divide k.
2
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
1,1
EXAMPLE
20 is in this list because 7 divides 21 but 6 does not divide 20.
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 *)
PROG
(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)
CROSSREFS
Sequence in context: A118358 A101731 A080765 * A257292 A234285 A314584
KEYWORD
nonn
AUTHOR
Peter Luschny, May 27 2013
STATUS
approved