A231370 Squarefree composite numbers k such that 2 is a primitive root for all prime factors of k.

15, 33, 39, 55, 57, 65, 87, 95, 111, 143, 145, 159, 165, 177, 183, 185, 195, 201, 209, 247, 249, 265, 285, 295, 303, 305, 319, 321, 335, 377, 393, 407, 415, 417, 429, 435, 447, 481, 489, 505, 519, 535, 537, 543, 551, 555, 583, 591, 627, 633, 649, 655, 671, 681

Offset

1,1

Comments

If k is the smallest integer satisfying 10^k == 1 (mod p), we say that 10 has order k (mod p). If n is the product of distinct primes p_i, the period of 1/n in base b is the least common multiple of the orders of b (mod p_i), provided b and n are relatively prime.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Primitive Root.

Wikipedia, Binary number.

Mathematica

q[n_] := CompositeQ[n] && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;; , 1]],  MultiplicativeOrder[2, #] == # - 1 &]; Select[Range[700], q] (* Amiram Eldar, Oct 03 2021 *)

Prog

(PARI) isok(k) = if ((k>1) && (k%2) && !isprime(k) && issquarefree(k), my(f=factor(k)[, 1]~); for (j=1, #f, if (znorder(Mod(2, f[j])) != (f[j]-1), return(0))); return (1)); return (0); \\ Michel Marcus, Oct 03 2021

Crossrefs

Subsequence of A024556.

Cf. A001122, A231371, A231372.

Sequence in context: A140608 A085371 A162887 * A246755 A212311 A262741

Adjacent sequences: A231367 A231368 A231369 * A231371 A231372 A231373

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 08 2013

Status

approved