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A119315 Numbers with composite numbers as third divisors.

%I A119315 #22 Jul 02 2022 14:38:22
%S A119315 4,8,9,16,20,25,27,28,32,40,44,49,52,56,64,68,76,80,81,88,92,99,100,
%T A119315 104,112,116,117,121,124,125,128,136,140,148,152,153,160,164,169,171,
%U A119315 172,176,184,188,196,200,207,208,212,220,224,232,236,243,244,248,256,260
%N A119315 Numbers with composite numbers as third divisors.
%C A119315 m is a term iff A067029(m) > 1 and (A001221(m) = 1 or A020639(m)^2 <= A119288(m)).
%C A119315 The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 3, 23, 221, 2194, 21895, 219307, 2193435, 21937419, 219396872, 2193979781, ... . Apparently, the asymptotic density of this sequence exists and equals 0.219... . - _Amiram Eldar_, Jul 02 2022
%C A119315 Numbers k such that A292269(k) is composite, which must then be a square of prime (A001248) by necessity. - _Antti Karttunen_, Jul 02 2022
%H A119315 Amiram Eldar, <a href="/A119315/b119315.txt">Table of n, a(n) for n = 1..10000</a>
%t A119315 Select[Range[300],CompositeQ[Divisors[#][[3]]]&]//Quiet (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 03 2021 *)
%t A119315 Select[Range[260], (f = FactorInteger[#])[[1, 2]] > 1 && (Length[f] == 1 || f[[1, 1]]^2 < f[[2, 1]]) &] (* _Amiram Eldar_, Jul 02 2022 *)
%o A119315 (PARI)
%o A119315 A355453(n) = ((n>1) && !isprime(n) && !isprime(divisors(n)[3]));
%o A119315 isA119315(n) = A355453(n); \\ _Antti Karttunen_, Jul 02 2022
%Y A119315 Complement of A119316.
%Y A119315 A025475, A092259, and A355445 are subsequences.
%Y A119315 Cf. A000005, A001221, A001248, A002808, A020639, A027750, A067029, A292269, A355453 (characteristic function).
%Y A119315 Cf. also A355455.
%K A119315 nonn
%O A119315 1,1
%A A119315 _Reinhard Zumkeller_, May 15 2006