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Number of primes less than prime(n)^prime(n).
0

%I #25 Sep 08 2022 08:45:11

%S 2,9,445,65685,11262113374,9373678643933,17547676024364306476,

%T 36020106660104388871845

%N Number of primes less than prime(n)^prime(n).

%F a(n) = A064151(prime(n)) = A000720(A051674(n)). - _Michel Marcus_, Mar 17 2015

%e There are 9 primes less than 3^3 = 27, namely 2,3,5,7,11,13,17,19,23. Since 3 is prime(2), a(2) = 9.

%t f[n_] := Block[{p = Prime@ n}, PrimePi[p^p]]; Array[f, 5] (* _Michael De Vlieger_, Mar 17 2015 *)

%o (PARI) primeslesspp(n) = /* primes less than p^p */ { forprime(x=2, n, y=primepi(x^x); print1(y", "); ); }

%o (Magma) [ #PrimesUpTo(NthPrime(n)^NthPrime(n)): n in [1..4] ]; // _Vincenzo Librandi_, Mar 17 2015

%Y Cf. A064151.

%K hard,more,nonn

%O 1,1

%A _Cino Hilliard_, Jul 28 2003

%E a(5)-a(7) from _David Baugh_, Mar 17 2015

%E a(8) from _Chai Wah Wu_, Apr 18 2018