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A085501 Number of prime powers p^k <= n that are not prime (k = 0 or k > 1). 4

%I

%S 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 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 10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11

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

%C a(n) = Max{k: A025475(k)<=n};

%C a(n)=A065515(n)-A000720(n)=A069637(n)+1;

%C for n<36=(2*3)^2: a(n) = A069623(n).

%H Charles R Greathouse IV, <a href="/A085501/b085501.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePower.html">Prime Power</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Powers</a>.

%o (PARI) a(n)=sum(k=2,logint(n,2), primepi(sqrtnint(n,k)))+1 \\ _Charles R Greathouse IV_, Jul 21 2017

%o (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

%K nonn,easy

%O 1,4

%A _Reinhard Zumkeller_, Jul 03 2003

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Last modified August 17 17:00 EDT 2019. Contains 326059 sequences. (Running on oeis4.)