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%I #15 Oct 03 2021 04:47:29
%S 119,133,161,203,323,329,391,413,427,437,493,551,667,679,763,791,799,
%T 893,917,1003,1037,1043,1081,1121,1159,1169,1253,1267,1351,1357,1363,
%U 1403,1561,1603,1631,1649,1711,1769,1799,1841,1843,1853,1883,1921,2071,2147,2191
%N Squarefree composite numbers k such that 10 is a primitive root for all prime factors of k.
%C 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.
%H Amiram Eldar, <a href="/A231372/b231372.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimitiveRoot.html">Primitive Root</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Decimal">Decimal</a>.
%t q[n_] := CompositeQ[n] && SquareFreeQ[n] && AllTrue[FactorInteger[n][[;;,1]], MultiplicativeOrder[10, #] == # - 1 &]; Select[Range[2000], q] (* _Amiram Eldar_, Oct 03 2021 *)
%Y Subsequence of A024556.
%Y Cf. A001913, A231370, A231371.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Nov 08 2013