A060970 Number of fourth powers of primes <= 2^n.

0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 8, 8, 9, 11, 12, 14, 16, 18, 21, 24, 28, 31, 36, 42, 47, 54, 62, 72, 82, 97, 111, 128, 149, 172, 199, 229, 268, 309, 360, 418, 481, 564, 651, 760, 886, 1028, 1201, 1393, 1629, 1900, 2211, 2585, 3010, 3512, 4104, 4792

Offset: 0

Author

Labos Elemer, May 09 2001

Keywords

• nonn

Examples

			For n = 12, the 4th powers of prime not exceeding 2^12 = 4096 are 16, 81, 625, 2401, so a(12) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..297
• Index entries for sequences related to numbers of primes in various ranges.

Crossrefs

Cf. A000720, A007053, A018048, A030514, A036386, A060967, A060969, A060971.

Programs

Mathematica

Table[ PrimePi[ Floor[ 2^(g/4)//N ] ], {g, 0, 100} ]

Formula

a(4*n) = A007053(n). - Chai Wah Wu, Jan 23 2025

a(n) = A000720(A018048(n)). - Amiram Eldar, Mar 22 2025

Extensions

Missing a(0)=0 inserted by Sean A. Irvine, Jan 09 2023