A086693 Number of primes less than prime(n)^prime(n).

2, 9, 445, 65685, 11262113374, 9373678643933, 17547676024364306476, 36020106660104388871845

Offset: 1

Author

Cino Hilliard, Jul 28 2003

Keywords

• hard
• more
• nonn

Examples

			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.
		

Crossrefs

Cf. A064151.

Programs

Magma

[ #PrimesUpTo(NthPrime(n)^NthPrime(n)): n in [1..4] ]; // Vincenzo Librandi, Mar 17 2015

Mathematica

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

PARI

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

Formula

a(n) = A064151(prime(n)) = A000720(A051674(n)). - Michel Marcus, Mar 17 2015

Extensions

a(5)-a(7) from David Baugh, Mar 17 2015

a(8) from Chai Wah Wu, Apr 18 2018