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%I #21 Aug 15 2022 08:34:51
%S 2,2,3,6,14,34,110,384,1540,7019,34501,183439,1045196,6164423,38285946
%N a(n) = pi((sqrt(P(n))+1)^2) - pi(P(n)), where pi(n) = number of primes <= n and P(n) = n-th primorial.
%C Conjecture: pi((sqrt(P(n))+1)^2) - pi(P(n)) >= n.
%t 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 *)
%o (PARI) a(n) = my(P=vecprod(primes(n))); primepi((sqrt(P)+1)^2) - primepi(P); \\ _Michel Marcus_, Aug 15 2022
%Y Cf. A000720 (pi), A002110 (primorials), A000849 (pi(primorials)).
%K nonn,more,less
%O 1,1
%A _Daniel Tisdale_, Oct 18 2009, Oct 23 2009
%E a(13)-a(15) from _Ray Chandler_, May 10 2010
%E Name edited by _Michel Marcus_, Aug 15 2022
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