A119316 - OEIS

%I #11 Jul 02 2022 09:29:03

%S 1,2,3,5,6,7,10,11,12,13,14,15,17,18,19,21,22,23,24,26,29,30,31,33,34,

%T 35,36,37,38,39,41,42,43,45,46,47,48,50,51,53,54,55,57,58,59,60,61,62,

%U 63,65,66,67,69,70,71,72,73,74,75,77,78,79,82,83,84,85,86,87,89,90,91

%N Complement of A119315.

%C m is a term iff A067029(m) = 1 or (A001221(m) > 1 and A119288(m) < A020639(m)^2).

%C The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 7, 77, 779, 7806, 78105, 780693, 7806565, 78062581, 780603128, 7806020219, ... . Apparently, the asymptotic density of this sequence exists and equals 0.780... . - _Amiram Eldar_, Jul 02 2022

%H Amiram Eldar, <a href="/A119316/b119316.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[100], (f = FactorInteger[#])[[1, 2]] == 1 || (Length[f] > 1 && f[[1, 1]]^2 > f[[2, 1]]) &] (* _Amiram Eldar_, Jul 02 2022 *)

%Y Union of A119313 and A008578.

%Y (Intersection with A119314) = A008578.

%Y Cf. A001221, A020639, A067029, A119288, A119315.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, May 15 2006