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A166678
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a(n) = pi((sqrt(P(n))+1)^2) - pi(P(n)), where pi(n) = number of primes <= n and P(n) = n-th primorial.
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0
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2, 2, 3, 6, 14, 34, 110, 384, 1540, 7019, 34501, 183439, 1045196, 6164423, 38285946
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OFFSET
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1,1
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COMMENTS
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Conjecture: pi((sqrt(P(n))+1)^2) - pi(P(n)) >= n.
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LINKS
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MATHEMATICA
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a[n_] := Product[Prime[k], {k, 1, n}]; Table[PrimePi[(Sqrt[a[n]] + 1)^2] - PrimePi[a[n]], {n, 1, 12}] (* G. C. Greubel, May 22 2016 *)
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PROG
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(PARI) a(n) = my(P=vecprod(primes(n))); primepi((sqrt(P)+1)^2) - primepi(P); \\ Michel Marcus, Aug 15 2022
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CROSSREFS
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KEYWORD
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nonn,more,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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