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

1,1

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

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 *)

Prog

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

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.

Sequence in context: A134344 A372740 A324278 * A346256 A010390 A003624

Adjacent sequences: A119312 A119313 A119314 * A119316 A119317 A119318

Keyword

nonn

Author

Reinhard Zumkeller, May 15 2006

Status

approved