A316992 Numbers m such that 1 < gcd(m, 15) < m and m does not divide 15^e for e >= 0.

6, 10, 12, 18, 20, 21, 24, 30, 33, 35, 36, 39, 40, 42, 48, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 78, 80, 84, 85, 87, 90, 93, 95, 96, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 120, 123, 126, 129, 130, 132, 138, 140, 141, 144, 145, 147, 150

Offset: 1

Author

Michael De Vlieger, Aug 02 2018

Keywords

• easy
• nonn

Comments

Complement of A000027 and union of A003593 and A229829.

Analogous to A081062 and A105115 that apply to A120944(1)=6 and A120944(2)=10, respectively.

This sequence applies to term A120944(4)=15.

Examples

			6 is in the sequence since gcd(6, 15) = 3 and 6 does not divide 15^e with integer e >= 0.
2 and 4 are not in the sequence since they are coprime to 15.
3 and 5 are not in the sequence since they are divisors of 15.
9 is not in the sequence since 9 | 15^2.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003593, A081062, A105115, A120944, A229829, A316991.

Programs

Mathematica

With[{nn = 150, k = 15}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]]