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A226038 Numbers n such that there are no primes p which divide n+1 and p-1 does not divide n. 3
0, 1, 2, 3, 4, 6, 7, 8, 10, 12, 15, 16, 18, 22, 24, 26, 28, 30, 31, 36, 40, 42, 44, 46, 48, 52, 58, 60, 63, 66, 70, 72, 78, 80, 82, 88, 96, 100, 102, 106, 108, 112, 120, 124, 126, 127, 130, 136, 138, 148, 150, 156, 162, 166, 168, 172, 178, 180, 190, 192, 196, 198 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

These are the numbers which satisfy the weak Clausen condition but not the Clausen condition.

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

Peter Luschny, Generalized Bernoulli numbers.

EXAMPLE

A counterexample is n = 14. 5 divides 15 but 4 does not divide 14.

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]));

A226038_list := n -> select(k -> [] = F(k), [$0..n]);

A226038_list(200);

MATHEMATICA

s[p_, n_] := Mod[n+1, p] == 0 && Mod[n, p-1] != 0; f[n_] := Select[ Select[ Range[n], PrimeQ], s[#, n] &]; A226038 = Select[ Range[0, 200], f[#] == {} &] (* Jean-François Alcover, Jul 29 2013, after Maple *)

Join[{0}, Select[Range[200], And @@ Divisible[#, FactorInteger[# + 1][[All, 1]] - 1] &]] (* Ivan Neretin, Aug 04 2016 *)

PROG

(Sage)

def F(n): return filter(lambda p: ((n+1) % p == 0) and (n % (p-1) != 0), primes(n))

def A226038_list(n): return list(filter(lambda n: not list(F(n)), (0..n)))

A226038_list(200)

CROSSREFS

Cf. A226039, A226040, A225481.

Sequence in context: A257282 A221178 A080389 * A181062 A091199 A093452

Adjacent sequences:  A226035 A226036 A226037 * A226039 A226040 A226041

KEYWORD

nonn

AUTHOR

Peter Luschny, May 27 2013

STATUS

approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)