

A238815


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


1



1, 8, 36, 194, 1281, 9701, 78735, 665135, 5762860, 50851224, 455062596, 4118082970, 37607992089, 346065767407, 3204942420924, 29844572385359, 279238346816393, 2623557174778439, 24739954338671300, 234057667428388199, 2220819603016308080, 21127269487386615272
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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 * A290357 A030112 A001555
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



