A060971 Number of fifth powers of primes <= 2^n.

0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 8, 9, 9, 11, 11, 13, 15, 16, 18, 21, 23, 25, 29, 31, 34, 39, 44, 47, 54, 62, 68, 76, 86, 97, 107, 122, 137, 154, 172, 193, 217, 244, 275, 309, 349, 393, 442, 499, 564, 635, 712, 807, 914, 1028, 1163, 1315, 1482

Offset: 0

Author

Labos Elemer, May 09 2001

Keywords

• nonn

Examples

			For n = 10: the 5th powers of primes not exceeding 2^10 = 1024 are 32 and 243, so a(10) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..377
• Index entries for sequences related to numbers of primes in various ranges.

Crossrefs

Cf. A000720, A007053, A018117, A036386, A050997, A060967, A060969, A060970.

Programs

Mathematica

Table[ PrimePi[ Floor[ 2^(g/5)//N ] ], {g, 0, 150} ]

Formula

a(5*n) = A007053(n). - Chai Wah Wu, Jan 23 2025

a(n) = A000720(A018117(n)). - Amiram Eldar, Mar 22 2025

Extensions

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