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 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] 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

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