A330137 - OEIS

%I #9 Dec 16 2019 11:48:15

%S 14,21,22,26,28,33,34,35,38,39,42,44,46,51,52,55,56,57,58,62,63,65,66,

%T 68,69,70,74,76,78,82,84,85,86,87,88,92,93,94,95,98,99,102,104,105,

%U 106,110,111,112,114,115,116,117,118,122,123,124,126,129,130,132,134

%N Numbers m such that 1 < gcd(m, 30) < m and m does not divide 30^e for e >= 0.

%C Numbers m that are neither 5-smooth nor reduced residues mod 30. Such numbers m have at least 1 prime factor p <= 5 and at least 1 prime factor q > 5.

%C Complement of the union of A007775 and A051037.

%C Analogous to A105115 for A120944(2) = 10. This sequence applies to the second primorial in A120944, i.e., 30 = A002110(2).

%H Michael De Vlieger, <a href="/A330137/b330137.txt">Table of n, a(n) for n = 1..10000</a>

%e 14 is in the sequence since gcd(14, 30) = 2 and 14 does not divide 30^e with integer e >= 0.

%e 15 is not in the sequence since 15 | 30.

%e 16 is not in the sequence since 16 | 30^4.

%e 17 is not in the sequence since 17 is coprime to 30.

%t With[{nn = 135, k = 30}, Select[Range@ nn, And[1 < GCD[#, k] < #, PowerMod[k, Floor@ Log2@ nn, #] != 0] &]]

%Y Cf. A002110, A007775, A051037, A105115, A120944, A306999, A307589, A316991, A316992, A330136.

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Dec 02 2019