|
| |
|
|
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
|
| |
|
|
