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

0,2

Links

Table of n, a(n) for n=0..21.

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006880, A076048, A267712.

Sequence in context: A054627 A019022 A079819 * A341543 A290357 A030112

Adjacent sequences: A238812 A238813 A238814 * A238816 A238817 A238818

Keyword

nonn

Author

Robert G. Wilson v, Mar 05 2014

Extensions

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

Status

approved