A119315 - OEIS

%I #22 Jul 02 2022 14:38:22

%S 4,8,9,16,20,25,27,28,32,40,44,49,52,56,64,68,76,80,81,88,92,99,100,

%T 104,112,116,117,121,124,125,128,136,140,148,152,153,160,164,169,171,

%U 172,176,184,188,196,200,207,208,212,220,224,232,236,243,244,248,256,260

%N Numbers with composite numbers as third divisors.

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

%C 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 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 Amiram Eldar, <a href="/A119315/b119315.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[300],CompositeQ[Divisors[#][[3]]]&]//Quiet (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 03 2021 *)

%t Select[Range[260], (f = FactorInteger[#])[[1, 2]] > 1 && (Length[f] == 1 || f[[1, 1]]^2 < f[[2, 1]]) &] (* _Amiram Eldar_, Jul 02 2022 *)

%o (PARI)

%o A355453(n) = ((n>1) && !isprime(n) && !isprime(divisors(n)[3]));

%o isA119315(n) = A355453(n); \\ _Antti Karttunen_, Jul 02 2022

%Y Complement of A119316.

%Y A025475, A092259, and A355445 are subsequences.

%Y Cf. A000005, A001221, A001248, A002808, A020639, A027750, A067029, A292269, A355453 (characteristic function).

%Y Cf. also A355455.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 15 2006