login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A119315 Numbers with composite numbers as third divisors. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A162215 A134344 A324278 * A346256 A010390 A003624

Adjacent sequences:  A119312 A119313 A119314 * A119316 A119317 A119318

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 15 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 18:04 EDT 2022. Contains 357002 sequences. (Running on oeis4.)