A334393 - OEIS

%I #33 Aug 13 2024 11:21:22

%S 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,

%T 61,67,71,73,79,83,89,97,101,103,107,109,113,121,125,127,128,131,137,

%U 139,149,151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241,243,251

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

%C First differs from A115975 at a(42). - _Omar E. Pol_, Apr 26 2020

%H Amiram Eldar, <a href="/A334393/b334393.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..218 from Kevin Foote)

%t Select[Range[250], Length[(f = FactorInteger[#])] == 1 && ((e = f[[1, 2]]) == 1 || PrimeQ[e]) &] (* _Amiram Eldar_, Apr 27 2020 *)

%o (PARI) isok(n) = if (n==1, return (1)); my(k=isprimepower(n)); (k==1) || isprime(k); \\ _Michel Marcus_, Apr 27 2020

%o (Python)

%o from sympy import primepi, integer_nthroot, primerange

%o def A334393(n):

%o     def f(x): return int(n-1+x-primepi(x)-sum(primepi(integer_nthroot(x, p)[0]) for p in primerange(x.bit_length())))

%o     m, k = n, f(n)

%o     while m != k:

%o         m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Aug 13 2024

%Y Union of A008578 and A053810.

%Y Cf. A115975.

%K nonn

%O 1,2

%A _Kevin Foote_, Apr 26 2020