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

6, 12, 14, 15, 18, 24, 28, 30, 33, 35, 36, 39, 42, 45, 48, 51, 54, 56, 57, 60, 66, 69, 70, 72, 75, 77, 78, 84, 87, 90, 91, 93, 96, 98, 99, 102, 105, 108, 111, 112, 114, 117, 119, 120, 123, 126, 129, 132, 133, 135, 138, 140, 141, 144, 150, 153, 154, 156, 159, 161

Offset: 1

Author

Michael De Vlieger, Aug 22 2019

Keywords

• nonn
• easy

Comments

Complement of the union of A003594 and A160545.

Analogous to A081062 and A105115 regarding terms 1 and 2 of A120944, respectively. This sequence applies to A120944(5) = 21.

Examples

			6 is in the sequence since gcd(6, 21) = 3 and 6 does not divide 21^e with integer e >= 0.
5 is not in the sequence since it is coprime to 21.
3 is not in the sequence since 3 | 21.
9 is not in the sequence since 9 | 21^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003594, A081062, A105115, A120944, A160545.

Programs

Maple

filter:= proc(n) local g;
  g:= igcd(n,21);
  if g = 1 or g = n then return false fi;
  3^padic:-ordp(n,3)*7^padic:-ordp(n,7) < n
end proc:
select(filter, [$1..200]); # Robert Israel, Aug 28 2019

Mathematica

With[{nn = 161, k = 21}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]]