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

1, 8, 36, 194, 1281, 9701, 78735, 665135, 5762860, 50851224, 455062596, 4118082970, 37607992089, 346065767407, 3204942420924, 29844572385359, 279238346816393, 2623557174778439, 24739954338671300, 234057667428388199, 2220819603016308080, 21127269487386615272

Offset: 0

Author

Robert G. Wilson v, Mar 05 2014

Keywords

• nonn

Crossrefs

Cf. A006880, A076048, A267712.

Programs

Mathematica

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

PARI

a(n)=sum(k=2,10^n,isprimepower(k)>0)+1 \\ Charles R Greathouse IV, Mar 05 2014

PARI

a(n)=sum(e=1,n*log(10)\log(2),primepi(sqrtnint(10^n,e)))+1 \\ Charles R Greathouse IV, Mar 05 2014

Formula

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

a(n) ~ 10^n/(n log 10). - Charles R Greathouse IV, Mar 05 2014

For n > 0, a(n) = A267712(n) + 1. - Jon E. Schoenfield, Apr 19 2018

Extensions

a(15)-a(21) from Charles R Greathouse IV, Mar 05 2014