A060967 Number of squared primes <= 2^n.

0, 0, 1, 1, 2, 3, 4, 5, 6, 8, 11, 14, 18, 24, 31, 42, 54, 72, 97, 128, 172, 229, 309, 418, 564, 760, 1028, 1393, 1900, 2585, 3512, 4792, 6542, 8952, 12251, 16777, 23000, 31579, 43390, 59631, 82025, 112957, 155611, 214516, 295947, 408493, 564163, 779638

Offset

0,5

Links

Amiram Eldar, Table of n, a(n) for n = 0..150 (terms 0..63 from Harry J. Smith, terms 64..112 from Hiroaki Yamanouchi, terms 113..125 from Ray Chandler)

Index entries for sequences related to numbers of primes in various ranges.

Formula

a(2*n) = A007053(n). - Amiram Eldar, Jul 10 2024

a(n) = A000720(A017910(n)). - Amiram Eldar, Mar 22 2025

Example

For n = 8, the squared primes not exceeding 2^8 = 256 are 4, 9, 25, 49, 121, 169, so a(8) = 6.

Mathematica

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

Prog

(PARI) a(n) = { primepi(sqrtint(2^n)) } \\ Harry J. Smith, Jul 15 2009

Crossrefs

Cf. A000720, A001248, A007053, A017910, A036386, A060969, A060970, A060971, A122121.

Sequence in context: A253773 A124067 A308806 * A218930 A350391 A026483

Adjacent sequences: A060964 A060965 A060966 * A060968 A060969 A060970

Keyword

nonn

Author

Labos Elemer, May 09 2001

Extensions

a(0) prepended by Harry J. Smith, Jul 15 2009

Status

approved