A334393 Numbers of the form p^q where p and q are either 1 or prime.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251

Offset: 1

Author

Kevin Foote, Apr 26 2020

Keywords

• nonn

Comments

First differs from A115975 at a(42). - Omar E. Pol, Apr 26 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..218 from Kevin Foote)

Crossrefs

Union of A008578 and A053810.

Cf. A115975.

Programs

Mathematica

Select[Range[250], Length[(f = FactorInteger[#])] == 1 && ((e = f[[1, 2]]) == 1 || PrimeQ[e]) &] (* Amiram Eldar, Apr 27 2020 *)

PARI

isok(n) = if (n==1, return (1)); my(k=isprimepower(n)); (k==1) || isprime(k); \\ Michel Marcus, Apr 27 2020

Python

from sympy import primepi, integer_nthroot, primerange
def A334393(n):
    def f(x): return int(n-1+x-primepi(x)-sum(primepi(integer_nthroot(x, p)[0]) for p in primerange(x.bit_length())))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m # Chai Wah Wu, Aug 13 2024