A225506 -2-Knödel numbers.

4, 6, 8, 10, 12, 24, 28, 30, 70, 88, 130, 238, 510, 754, 868, 910, 1330, 2068, 2590, 2728, 3304, 4002, 5110, 5406, 8554, 8710, 12958, 15748, 18430, 20878, 21238, 23902, 24178, 32422, 39928, 46870, 49210, 53590, 55678, 57358, 62248, 67858, 70414, 79378, 88198, 95038, 95758, 95788, 102238, 114478

Offset: 1

Author

Paolo P. Lava, May 09 2013

Keywords

• nonn

Comments

Extension of k-Knödel numbers to k negative, in this case equal to -2. Composite numbers n > 0 such that if 1 < a < n and gcd(n,a) = 1 then a^(n+2) = 1 mod n.

All terms are even numbers.

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Knödel Numbers

Crossrefs

Cf. A208728.

Cf. A225507, A225508, A225509, A225510, A225511, A225512, A225513, A225514.

Programs

Maple

with(numtheory); ListA225506:=proc(q,k) local a,n,ok;
for n from 2 to q do if not isprime(n) then ok:=1; for a from 1 to n do
if gcd(a,n)=1 then if (a^(n-k)-1) mod n<>0 then ok:=0; break; fi; fi;
od; if ok=1 then print(n); fi; fi; od; end: ListA225506(10^6,-2);

Mathematica

Select[Range[10000], CompositeQ[#] && Divisible[# + 2, CarmichaelLambda[#]] &] (* Amiram Eldar, Mar 28 2019 *)

PARI

is(n) = forprime(p=3, n, if (n%p != 0 && Mod(p,n)^(n+2) != 1, return(0))); 1;
seq(N) = {
  my(a=vector(N), k=0, n=4);
  while(k < N, if(is(n), a[k++] = n); n += 2);
  a;
};
seq(50) \\ Gheorghe Coserea, Dec 23 2018

Extensions

More terms from Gheorghe Coserea, Dec 23 2018