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Number of squared primes <= 2^n.
14

%I #37 Jul 10 2024 02:57:26

%S 0,0,1,1,2,3,4,5,6,8,11,14,18,24,31,42,54,72,97,128,172,229,309,418,

%T 564,760,1028,1393,1900,2585,3512,4792,6542,8952,12251,16777,23000,

%U 31579,43390,59631,82025,112957,155611,214516,295947,408493,564163,779638

%N Number of squared primes <= 2^n.

%H Ray Chandler, <a href="/A060967/b060967.txt">Table of n, a(n) for n = 0..125</a> (terms 0..63 from Harry J. Smith, terms 64..112 from Hiroaki Yamanouchi)

%F a(2*n) = A007053(n). - _Amiram Eldar_, Jul 10 2024

%e For n = 8, the squared primes not exceeding 256 are 4, 9, 25, 49, 121, 169 so a(8) = 6.

%t Table[ PrimePi[ Floor[ 2^(g/2)//N ] ], {g, 1, 75} ]

%o (PARI) { f="b060967.txt"; default(primelimit, 4294965247); a=n=-1; s=1; forprime (p=2, 4294965247, a++; if (p^2>s, write(f, n++, " ", a); s*=2); if (p^2>s, write(f, n++, " ", a); s*=2); ) } \\ _Harry J. Smith_, Jul 15 2009

%Y Cf. A007053, A036386.

%K nonn

%O 0,5

%A _Labos Elemer_, May 09 2001

%E a(0) prepended by _Harry J. Smith_, Jul 15 2009