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A306999 Numbers m such that 1 < gcd(m, 21) < m and m does not divide 21^e for e >= 0.

%I A306999 #13 Oct 04 2019 07:43:36
%S A306999 6,12,14,15,18,24,28,30,33,35,36,39,42,45,48,51,54,56,57,60,66,69,70,
%T A306999 72,75,77,78,84,87,90,91,93,96,98,99,102,105,108,111,112,114,117,119,
%U A306999 120,123,126,129,132,133,135,138,140,141,144,150,153,154,156,159,161
%N A306999 Numbers m such that 1 < gcd(m, 21) < m and m does not divide 21^e for e >= 0.
%C A306999 Complement of the union of A003594 and A160545.
%C A306999 Analogous to A081062 and A105115 regarding terms 1 and 2 of A120944, respectively. This sequence applies to A120944(5) = 21.
%H A306999 Robert Israel, <a href="/A306999/b306999.txt">Table of n, a(n) for n = 1..10000</a>
%e A306999 6 is in the sequence since gcd(6, 21) = 3 and 6 does not divide 21^e with integer e >= 0.
%e A306999 5 is not in the sequence since it is coprime to 21.
%e A306999 3 is not in the sequence since 3 | 21.
%e A306999 9 is not in the sequence since 9 | 21^2.
%p A306999 filter:= proc(n) local g;
%p A306999   g:= igcd(n,21);
%p A306999   if g = 1 or g = n then return false fi;
%p A306999   3^padic:-ordp(n,3)*7^padic:-ordp(n,7) < n
%p A306999 end proc:
%p A306999 select(filter, [$1..200]); # _Robert Israel_, Aug 28 2019
%t A306999 With[{nn = 161, k = 21}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]]
%Y A306999 Cf. A003594, A081062, A105115, A120944, A160545.
%K A306999 nonn,easy
%O A306999 1,1
%A A306999 _Michael De Vlieger_, Aug 22 2019