A380332 a(n) = number of primes between n^2 and n^4.

0, 0, 4, 18, 48, 105, 199, 342, 546, 825, 1204, 1685, 2300, 3068, 4008, 5143, 6488, 8091, 9956, 12115, 14605, 17446, 20676, 24322, 28441, 33004, 38114, 43805, 50066, 56951, 64529, 72830, 81853, 91751, 102397, 114004, 126516, 140016, 154559, 170186, 186883, 204880, 224009, 244527, 266283, 289506, 314148, 340292, 368114, 397407

Offset: 0

Author

Clark Kimberling, Jan 26 2025

Keywords

• nonn

Comments

p(2) = 4 because there are 4 primes between 4 and 16.

Crossrefs

Cf. A000040, A000720, A038107, A079648, A380331.

Programs

Mathematica

Table[PrimePi[n^4] - PrimePi[n^2], {n, 0, 60}]

PARI

a(n) = primepi(n^4) - primepi(n^2); \\ Michel Marcus, Jan 27 2025

Python

from sympy import primepi
def A380332(n): return -primepi(m:=n**2)+primepi(m**2) # Chai Wah Wu, Jan 27 2025

Formula

a(n) = PrimePi(n^4) - PrimePi(n^2).