cp's OEIS Frontend

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

%I A334393 #33 Aug 13 2024 11:21:22
%S A334393 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 A334393 61,67,71,73,79,83,89,97,101,103,107,109,113,121,125,127,128,131,137,
%U A334393 139,149,151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229,233,239,241,243,251
%N A334393 Numbers of the form p^q where p and q are either 1 or prime.
%C A334393 First differs from A115975 at a(42). - _Omar E. Pol_, Apr 26 2020
%H A334393 Amiram Eldar, <a href="/A334393/b334393.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..218 from Kevin Foote)
%t A334393 Select[Range[250], Length[(f = FactorInteger[#])] == 1 && ((e = f[[1, 2]]) == 1 || PrimeQ[e]) &] (* _Amiram Eldar_, Apr 27 2020 *)
%o A334393 (PARI) isok(n) = if (n==1, return (1)); my(k=isprimepower(n)); (k==1) || isprime(k); \\ _Michel Marcus_, Apr 27 2020
%o A334393 (Python)
%o A334393 from sympy import primepi, integer_nthroot, primerange
%o A334393 def A334393(n):
%o A334393     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 A334393     m, k = n, f(n)
%o A334393     while m != k:
%o A334393         m, k = k, f(k)
%o A334393     return m # _Chai Wah Wu_, Aug 13 2024
%Y A334393 Union of A008578 and A053810.
%Y A334393 Cf. A115975.
%K A334393 nonn
%O A334393 1,2
%A A334393 _Kevin Foote_, Apr 26 2020