cp's OEIS Frontend

A085501 Number of prime powers p^k <= n that are not prime (k = 0 or k > 1).

%I A085501 #11 Feb 16 2025 08:32:50
%S A085501 1,1,1,2,2,2,2,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,7,7,7,7,7,8,8,8,
%T A085501 8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,
%U A085501 10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11
%N A085501 Number of prime powers p^k <= n that are not prime (k = 0 or k > 1).
%C A085501 a(n) = Max{k: A025475(k)<=n};
%C A085501 a(n)=A065515(n)-A000720(n)=A069637(n)+1;
%C A085501 for n<36=(2*3)^2: a(n) = A069623(n).
%H A085501 Charles R Greathouse IV, <a href="/A085501/b085501.txt">Table of n, a(n) for n = 1..10000</a>
%H A085501 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimePower.html">Prime Power</a>.
%H A085501 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">Perfect Powers</a>.
%o A085501 (PARI) a(n)=sum(k=2,logint(n,2), primepi(sqrtnint(n,k)))+1 \\ _Charles R Greathouse IV_, Jul 21 2017
%o A085501 (PARI) first(n)=my(v=vector(n),s=1); for(e=2,logint(n,2), forprime(p=2,sqrtnint(n,e), v[p^e]=1)); for(i=1,n, s+=v[i]; v[i]=s); v \\ _Charles R Greathouse IV_, Jul 21 2017
%o A085501 (Python)
%o A085501 from sympy import primepi, integer_nthroot
%o A085501 def A085501(n): return 1+sum(primepi(integer_nthroot(n,k)[0]) for k in range(2,n.bit_length())) # _Chai Wah Wu_, Aug 15 2024
%K A085501 nonn,easy
%O A085501 1,4
%A A085501 _Reinhard Zumkeller_, Jul 03 2003