A231371 -id:A231371 - cp's OEIS frontend

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

Arkadiusz Wesolowski, Nov 08 2013

nonn

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.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Root.
Wikipedia, Binary number.

Subsequence of A024556.

Cf. A001122, A231371, A231372.

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

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

A231372 Squarefree composite numbers k such that 10 is a primitive root for all prime factors of k.

Original entry on oeis.org

119, 133, 161, 203, 323, 329, 391, 413, 427, 437, 493, 551, 667, 679, 763, 791, 799, 893, 917, 1003, 1037, 1043, 1081, 1121, 1159, 1169, 1253, 1267, 1351, 1357, 1363, 1403, 1561, 1603, 1631, 1649, 1711, 1769, 1799, 1841, 1843, 1853, 1883, 1921, 2071, 2147, 2191

Offset: 1

Arkadiusz Wesolowski, Nov 08 2013

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Root.
Wikipedia, Decimal.

Subsequence of A024556.

Cf. A001913, A231370, A231371.

q[n_] := CompositeQ[n] && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;;,1]],  MultiplicativeOrder[10, #] == # - 1 &]; Select[Range[2000], q] (* Amiram Eldar, Oct 03 2021 *)

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI