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 A079648 Number of primes between n^2 and n^3. 2
 0, 0, 2, 5, 12, 21, 36, 53, 79, 107, 143, 187, 235, 288, 356, 428, 510, 595, 699, 810, 929, 1062, 1206, 1358, 1528, 1707, 1898, 2098, 2323, 2561, 2807, 3066, 3340, 3636, 3946, 4283, 4611, 4975, 5351, 5755, 6162, 6587, 7034, 7506, 7998, 8504, 9042, 9587, 10157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS There is always a prime between n^2 and n^3 for n > 1. For n = 2, primes 5 and 7 are between 4 and 8. For n > 2, we have the number of primes between n^2 and n^3 ~ n^3/log(n^3) - n^2/log(n^2) = n^2*(2n-3)/(6*log(n)) -> infinity as n -> infinity. A corollary to this is that the number of primes is infinite. Number of primes in row n of the triangle in A214084; a(n) = Sum_{m=n^2..n^3} A010051(m). - Reinhard Zumkeller, Jul 07 2012 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..110 EXAMPLE For n = 4 4^2 = 16, 4^3 = 64. there are 12 primes between 16 and 64 namely, 17,19,23,29,31,37,41,43,47,53,59,61. PROG (PARI) /* Count primes between x^2 and x^3. */ primex2x3(m, n) = { local(x, y, c); for(x=m, n, c=0; for(y=x^2, x^3, if(ispseudoprime(y), c++) ); print(c) ) } (Haskell) a079648 = sum . map a010051 . a214084_row  -- Reinhard Zumkeller, Jul 07 2012 CROSSREFS Sequence in context: A258602 A327065 A307605 * A080838 A244396 A182993 Adjacent sequences:  A079645 A079646 A079647 * A079649 A079650 A079651 KEYWORD nonn AUTHOR Cino Hilliard, Jan 22 2003, Aug 23 2007 EXTENSIONS Edited by N. J. A. Sloane, Aug 22 2009 at the suggestion of Richard Stanley STATUS approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)