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A238815 Number of prime powers p^k (k >= 0) (A000961) <= 10^n. 1

%I

%S 1,8,36,194,1281,9701,78735,665135,5762860,50851224,455062596,

%T 4118082970,37607992089,346065767407,3204942420924,29844572385359,

%U 279238346816393,2623557174778439,24739954338671300,234057667428388199,2220819603016308080,21127269487386615272

%N Number of prime powers p^k (k >= 0) (A000961) <= 10^n.

%F a(n) = A076048(n) + A006880(n).

%F a(n) ~ 10^n/(n log 10). - _Charles R Greathouse IV_, Mar 05 2014

%F For n > 0, a(n) = A267712(n) + 1. - _Jon E. Schoenfield_, Apr 19 2018

%t f[n_] := Block[{k = t = 1}, While[s = PrimePi[ 10^(n/k)]; s != 0, t = t + s; k++]; t]; Array[f, 15, 0]

%o (PARI) a(n)=sum(k=2,10^n,isprimepower(k)>0)+1 \\ _Charles R Greathouse IV_, Mar 05 2014

%o (PARI) a(n)=sum(e=1,n*log(10)\log(2),primepi(sqrtnint(10^n,e)))+1 \\ _Charles R Greathouse IV_, Mar 05 2014

%Y Cf. A006880, A076048, A267712.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Mar 05 2014

%E a(15)-a(21) from _Charles R Greathouse IV_, Mar 05 2014

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Last modified January 26 23:05 EST 2020. Contains 331289 sequences. (Running on oeis4.)