This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A070428 #42 Feb 16 2025 08:32:46
%S A070428 1,4,13,41,125,367,1111,3395,10491,32670,102231,320990,1010196,
%T A070428 3184138,10046921,31723592,100216745,316694005,1001003332,3164437425,
%U A070428 10004650118,31632790244,100021566157,316274216762,1000100055684
%N A070428 Number of perfect powers (A001597) not exceeding 10^n.
%C A070428 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 A070428 The Dominion (Wellington, NZ), 'wtd sell', 9 Nov. 1991.
%D A070428 sci.math, powers not exceeding n. nz science monthly advt, March 1993, 1:80 integers 1..10000 is perfect square or higher power.
%H A070428 Chai Wah Wu, <a href="/A070428/b070428.txt">Table of n, a(n) for n = 0..1999</a> (terms 0..999 from Robert G. Wilson v)
%H A070428 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>
%F A070428 a(n) ~ sqrt(10^n).
%e A070428 a(1) = 4 because the powers 1, 4, 8, 9 do not exceed 10^1.
%e A070428 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 A070428 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 A070428 (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
%o A070428 (Python)
%o A070428 from sympy import mobius, integer_nthroot
%o A070428 def A070428(n): return int(1-sum(mobius(x)*(integer_nthroot(10**n,x)[0]-1) for x in range(2,(10**n).bit_length()))) # _Chai Wah Wu_, Aug 13 2024
%Y A070428 Cf. A001597.
%Y A070428 Cf. A089579, A089580 (number of perfect powers (not including 1) < 10^n).
%K A070428 easy,nonn
%O A070428 0,2
%A A070428 _Donald S. McDonald_, May 15 2002
%E A070428 More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2002
%E A070428 Edited and extended by _Robert G. Wilson v_, Oct 11 2002