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!)
A138109 Positive integers n whose smallest prime factor is greater than the cube root of n and strictly less than the square root of n. 2
6, 15, 21, 35, 55, 65, 77, 85, 91, 95, 115, 119, 133, 143, 161, 187, 203, 209, 217, 221, 247, 253, 259, 287, 299, 301, 319, 323, 329, 341, 377, 391, 403, 407, 437, 451, 473, 481, 493, 517, 527, 533, 551, 559, 583, 589, 611, 629, 649, 667, 671, 689, 697, 703 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence was suggested by Moshe Shmuel Newman.

A020639(n)^2 < a(n) < A020639(n)^3. - Reinhard Zumkeller, Dec 17 2014

In other words, a(n) = pq with primes p, q satisfying p < q < p^2. - Charles R Greathouse IV, Apr 03 2017

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1)=6 because the smallest prime factor of 6 is 2 and 1.817...<2<2.449...

MATHEMATICA

s = {}; Do[f = FactorInteger[i]; test = f[[1]][[1]]; If [test < N[i^(1/2)] && test > N[i^(1/3)], s = Union[s, {i}]], {i, 2, 2000}]; Print[s]

Select[Range[1000], Surd[#, 3]<FactorInteger[#][[1, 1]]<Sqrt[#]&] (* Harvey P. Dale, May 10 2015 *)

PROG

(Haskell)

a138109 n = a138109_list !! (n-1)

a138109_list = filter f [1..] where

   f x = p ^ 2 < x && x < p ^ 3 where p = a020639 x

-- Reinhard Zumkeller, Dec 17 2014

(PARI) is(n)=my(f=factor(n)); f[, 2]==[1, 1]~ && f[1, 1]^3 > n \\ Charles R Greathouse IV, Mar 28 2017

(PARI) list(lim)=if(lim<6, return([])); my(v=List([6])); forprime(p=3, sqrtint(1+lim\=1)-1, forprime(q=p+2, min(p^2-2, lim\p), listput(v, p*q))); Set(v) \\ Charles R Greathouse IV, Mar 28 2017

CROSSREFS

Subsequence of A251728 and of A006881.

Cf. A020639.

Sequence in context: A015793 A261078 A063466 * A332877 A072521 A130178

Adjacent sequences:  A138106 A138107 A138108 * A138110 A138111 A138112

KEYWORD

nonn

AUTHOR

David S. Newman, May 04 2008

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 May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)