A383263 Union of prime powers (A246655) and numbers that are not squarefree (A013929).

2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 36, 37, 40, 41, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 56, 59, 60, 61, 63, 64, 67, 68, 71, 72, 73, 75, 76, 79, 80, 81, 83, 84, 88, 89, 90, 92, 96, 97, 98, 99, 100, 101, 103

Offset: 1

Author

Peter Luschny, Apr 27 2025

Keywords

• nonn

Comments

Union of A013929 and A000040. - Chai Wah Wu, Apr 27 2025

Crossrefs

Cf. A000040, A013929, A246655.

Essentially the same as A363597.

Programs

Maple

with(NumberTheory):
IsPrimePower := n -> nops(PrimeFactors(n)) = 1:
IsA383263 := n -> IsPrimePower(n) or not IsSquareFree(n):
select(IsA383263, [seq(1..104)]);

Mathematica

Select[Range[120], Or[PrimePowerQ[#], ! SquareFreeQ[#]] &] (* Michael De Vlieger, Apr 27 2025 *)

PARI

isok(k) = isprimepower(k) || !issquarefree(k);

Python

from math import isqrt
from sympy import mobius, primepi
def A383263(n):
    def f(x): return int(n+x+sum(mobius(k)*(x//k**2) for k in range(2, isqrt(x)+1))-primepi(x))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Apr 27 2025

SageMath

def isA383263(n: int) -> bool: return is_prime_power(n) or not is_squarefree(n)