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 A128930 Prime(n) * pi(n). 3
 0, 3, 10, 14, 33, 39, 68, 76, 92, 116, 155, 185, 246, 258, 282, 318, 413, 427, 536, 568, 584, 632, 747, 801, 873, 909, 927, 963, 1090, 1130, 1397, 1441, 1507, 1529, 1639, 1661, 1884, 1956, 2004, 2076, 2327, 2353, 2674, 2702, 2758, 2786, 3165, 3345, 3405 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Pi(n) = number of prime numbers <= n (A000720). Prime(n) = A000040(n). Conjecture: For each n there is at least one prime p such that a(n) < p < a(n+1). From the conjecture follows that the prime gaps g(n) = p(n+1) - p(n) = O(sqrt(p(n))/log(p(n))). Legendre's hypothesis is that g(n) = O(sqrt(p(n))). - Thomas Ordowski, Aug 11 2012 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Wikipedia, Legendre's conjecture FORMULA a(n) ~ (n log n)*(n/log n) = n^2. a(n) > n^2 for n > 4. - Thomas Ordowski, Aug 09 2012 MATHEMATICA Table[Prime[n] * PrimePi[n], {n, 50} (* Harvey P. Dale, Mar 17 2011 *) PROG (PARI) g(n) = for(x=1, n, y=prime(x)*primepi(x); print1(y", ")) CROSSREFS Cf. A000040, A000720, A128913. Sequence in context: A245524 A023866 A024593 * A328091 A048852 A226101 Adjacent sequences:  A128927 A128928 A128929 * A128931 A128932 A128933 KEYWORD easy,nonn AUTHOR Cino Hilliard, Apr 23 2007 STATUS approved

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Last modified September 23 12:43 EDT 2021. Contains 347617 sequences. (Running on oeis4.)