A119315 Numbers with composite numbers as third divisors.

4, 8, 9, 16, 20, 25, 27, 28, 32, 40, 44, 49, 52, 56, 64, 68, 76, 80, 81, 88, 92, 99, 100, 104, 112, 116, 117, 121, 124, 125, 128, 136, 140, 148, 152, 153, 160, 164, 169, 171, 172, 176, 184, 188, 196, 200, 207, 208, 212, 220, 224, 232, 236, 243, 244, 248, 256, 260

Offset: 1

Author

Reinhard Zumkeller, May 15 2006

Keywords

• nonn

Comments

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

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

Numbers k such that A292269(k) is composite, which must then be a square of prime (A001248) by necessity. - Antti Karttunen, Jul 02 2022

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A119316.

A025475, A092259, and A355445 are subsequences.

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

Cf. also A355455.

Programs

Mathematica

Select[Range[300],CompositeQ[Divisors[#][[3]]]&]//Quiet (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 03 2021 *)
Select[Range[260], (f = FactorInteger[#])[[1, 2]] > 1 && (Length[f] == 1 || f[[1, 1]]^2 < f[[2, 1]]) &] (* Amiram Eldar, Jul 02 2022 *)

PARI

A355453(n) = ((n>1) && !isprime(n) && !isprime(divisors(n)[3]));
isA119315(n) = A355453(n); \\ Antti Karttunen, Jul 02 2022