A380331 a(n) = number of primes < n^4.

0, 0, 6, 22, 54, 114, 210, 357, 564, 847, 1229, 1715, 2334, 3107, 4052, 5191, 6542, 8152, 10022, 12187, 14683, 17531, 20768, 24421, 28546, 33118, 38236, 43934, 50203, 57097, 64683, 72992, 82025, 91932, 102588, 114204, 126726, 140235, 154787, 170426, 187134

Offset: 0

Author

Clark Kimberling, Jan 21 2025

Keywords

• nonn

Examples

			a(2) = 6 because there are 6 primes < 16.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Subsequence of A038107, and hence of A000720.

Cf. A000040, A000583.

Programs

Mathematica

Table[PrimePi[n^4], {n, 0, 60}]

PARI

a(n)=primepi(n^4) \\ Charles R Greathouse IV, Jan 21 2025

Python

from sympy import primepi
def A380331(n): return primepi(n**4) # Chai Wah Wu, Jan 23 2025

Formula

a(n) = A000720(A000583(n)). - Pontus von Brömssen, Jan 21 2025

a(n) ~ (1/4)*n^4/log n. - Charles R Greathouse IV, Jan 23 2025