A087797 Primes, squares of primes and cubes of primes.

2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241

Offset: 1

Author

Benoit Cloitre, Oct 10 2003

Keywords

• nonn

Comments

Union of A000040 and A168363. - Chai Wah Wu, Aug 09 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000430, A002760, A168363.

Programs

Mathematica

m=400;Union[Prime[Range[PrimePi[m]]],Prime[Range[PrimePi[m^(1/2)]]]^2,Prime[Range[PrimePi[m^(1/3)]]]^3] (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)
With[{nn=70},Take[Union[Flatten[{#,#^2,#^3}&/@Prime[Range[nn]]]],nn]] (* Harvey P. Dale, Oct 16 2012 *)

PARI

is(n)=my(t=isprimepower(n)); t && t<4 \\ Charles R Greathouse IV, Oct 19 2015

Python

from math import isqrt
from sympy import primepi, integer_nthroot
def A087797(n):
    def f(x): return n+x-primepi(x)-primepi(isqrt(x))-primepi(integer_nthroot(x,3)[0])
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return int(m) # Chai Wah Wu, Aug 09 2024

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Oct 19 2015