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

%I A383263 #18 Apr 30 2025 13:53:02
%S A383263 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,
%T A383263 40,41,43,44,45,47,48,49,50,52,53,54,56,59,60,61,63,64,67,68,71,72,73,
%U A383263 75,76,79,80,81,83,84,88,89,90,92,96,97,98,99,100,101,103
%N A383263 Union of prime powers (A246655) and numbers that are not squarefree (A013929).
%C A383263 Union of A013929 and A000040. - _Chai Wah Wu_, Apr 27 2025
%p A383263 with(NumberTheory):
%p A383263 IsPrimePower := n -> nops(PrimeFactors(n)) = 1:
%p A383263 IsA383263 := n -> IsPrimePower(n) or not IsSquareFree(n):
%p A383263 select(IsA383263, [seq(1..104)]);
%t A383263 Select[Range[120], Or[PrimePowerQ[#], ! SquareFreeQ[#]] &] (* _Michael De Vlieger_, Apr 27 2025 *)
%o A383263 (SageMath)
%o A383263 def isA383263(n: int) -> bool: return is_prime_power(n) or not is_squarefree(n)
%o A383263 (PARI)
%o A383263 isok(k) = isprimepower(k) || !issquarefree(k);
%o A383263 (Python)
%o A383263 from math import isqrt
%o A383263 from sympy import mobius, primepi
%o A383263 def A383263(n):
%o A383263     def f(x): return int(n+x+sum(mobius(k)*(x//k**2) for k in range(2, isqrt(x)+1))-primepi(x))
%o A383263     m, k = n, f(n)
%o A383263     while m != k: m, k = k, f(k)
%o A383263     return m # _Chai Wah Wu_, Apr 27 2025
%Y A383263 Cf. A000040, A013929, A246655.
%Y A383263 Essentially the same as A363597.
%K A383263 nonn
%O A383263 1,1
%A A383263 _Peter Luschny_, Apr 27 2025