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A128913
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a(n) = n*pi(n).
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3
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0, 2, 6, 8, 15, 18, 28, 32, 36, 40, 55, 60, 78, 84, 90, 96, 119, 126, 152, 160, 168, 176, 207, 216, 225, 234, 243, 252, 290, 300, 341, 352, 363, 374, 385, 396, 444, 456, 468, 480, 533, 546, 602, 616, 630, 644, 705, 720, 735, 750, 765, 780, 848, 864, 880, 896
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OFFSET
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1,2
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COMMENTS
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Pi(n) = number of primes <= n (see A000720).
Conjecture: For each n there is at least one prime p such that 2*a(n) < p < 2*a(n+1). From the conjecture follows that the prime gaps g(n) = prime(n+1) - prime(n) = O(sqrt(prime(n)/log(prime(n)))). - Thomas Ordowski, Aug 12 2012
Number of primes that are obtained when listing all reduced fractions i/j with 1<=i,j<=n. - Michel Marcus, Sep 09 2015
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LINKS
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FORMULA
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G.f.: x*f'(x), where f(x) = Sum_{k>=1} x^prime(k)/(1 - x). - Ilya Gutkovskiy, Apr 10 2017
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EXAMPLE
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a(7) = 28 because there are four primes less than or equal to 7 (namely 2, 3, 5, 7) and 7 * 4 = 28.
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MATHEMATICA
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PROG
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(PARI) g(n) = for(x=1, n, y=x*primepi(x); print1(y", "))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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