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%I #31 Mar 02 2020 09:19:36
%S 1,4,13,41,125,367,1111,3395,10491,32670,102231,320990,1010196,
%T 3184138,10046921,31723592,100216745,316694005,1001003332,3164437425,
%U 10004650118,31632790244,100021566157,316274216762,1000100055684
%N Number of perfect powers (A001597) not exceeding 10^n.
%C In the programs for this sequence, 4*n can be replaced by the smaller floor(n*log(10)/log(2)). - _T. D. Noe_, Nov 17 2006
%D The Dominion (Wellington, NZ), 'wtd sell', 9 Nov. 1991.
%D sci.math, powers not exceeding n. nz science monthly advt, March 1993, 1:80 integers 1..10000 is perfect square or higher power.
%H Robert G. Wilson v, <a href="/A070428/b070428.txt">Table of n, a(n) for n = 0..999</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>
%F a(n) ~ sqrt(10^n).
%e a(1) = 4 because the powers 1, 4, 8, 9 do not exceed 10^1.
%e a(2) = 13 because 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81 & 100, are the only perfect power numbers less than or equal to 100.
%t f[n_] := 1 - Sum[ MoebiusMu[x]*Floor[10^(n/x) - 1], {x, 2, n*Log2[10]}]; Array[f, 25, 0] (* _Robert G. Wilson v_, May 22 2009; modified Aug 04 2014 *)
%o (PARI) for(n=0, 25, print1(sum(x=2, 4*n,-moebius(x)*(floor(10^(n/x)-1)))+1, ", ")); \\ Slightly modified by _Jinyuan Wang_, Mar 02 2020
%Y Cf. A001597.
%Y Cf. A089579, A089580 (number of perfect powers (not including 1) < 10^n).
%K easy,nonn
%O 0,2
%A _Donald S. McDonald_, May 15 2002
%E More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2002
%E Edited and extended by _Robert G. Wilson v_, Oct 11 2002
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