A379568 Number of n-digit numbers that have exactly 5 divisors.

0, 2, 1, 1, 3, 4, 5, 9, 15, 25, 37, 66, 107, 171, 293, 490, 810, 1362, 2302, 3889, 6552, 11149, 18950, 32255, 55053, 94096, 161036, 275896, 473709, 813669, 1399593, 2409905, 4154437, 7166774, 12375776, 21389092, 36994679, 64034719, 110918422, 192257157, 333449674, 578697626

Offset: 1

Author

Seiichi Manyama, Dec 26 2024

Keywords

• nonn
• base

Comments

A number has exactly 5 divisors if and only if it is the fourth power of a prime. - David Radcliffe, Dec 29 2024

Links

• David Radcliffe, Table of n, a(n) for n = 1..57

Crossrefs

Column k=5 of A284398.

Cf. A006880, A379566.

Programs

Mathematica

Table[PrimePi[10^(n/4)]-PrimePi[10^((n-1)/4)],{n,50}] (* Vincenzo Librandi, Dec 30 2024 *)

Python

from sympy import primepi
def a379568(n): return primepi(10**(n/4)) - primepi(10**((n-1)/4)) # David Radcliffe, Dec 29 2024

Formula

a(n) = PrimePi(10^(n/4)) - PrimePi(10^((n-1)/4)). - David Radcliffe, Dec 29 2024

Extensions

a(36)-a(42) from David Radcliffe, Dec 29 2024