A231371 Squarefree composite numbers k such that 8 is a primitive root for all prime factors of k.

15, 33, 55, 87, 145, 159, 165, 177, 249, 265, 295, 303, 319, 321, 393, 415, 435, 447, 505, 519, 535, 537, 583, 591, 649, 655, 681, 745, 795, 807, 865, 879, 885, 895, 913, 951, 957, 985, 1041, 1111, 1135, 1167, 1177, 1245, 1257, 1329, 1345, 1383, 1401, 1441

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, Octal.

Mathematica

q[n_] := CompositeQ[n] && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;; , 1]],  MultiplicativeOrder[8, #] == # - 1 &]; Select[Range[1441], q] (* Amiram Eldar, Oct 03 2021 *)

Crossrefs

Subsequence of A024556.

Cf. A019338, A231370, A231372.

Sequence in context: A071965 A242677 A020184 * A228318 A228321 A277385

Adjacent sequences: A231368 A231369 A231370 * A231372 A231373 A231374

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 08 2013

Status

approved