Search: id:A070428
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%I A070428
%S A070428 1,4,13,41,125,367,1111,3395,10491,32670,102231,320990,1010196,3184138,
%T A070428 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 a(n)=~sqrt(10^n).
%C A070428 In the programs for this sequence, 4n can be replaced by the smaller 
               floor(n*log(10)/log(2)) - T. D. Noe (noe(AT)sspectra.com), 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 Robert G. Wilson v, <a href="b070428.txt">Table of n, a(n) for n = 1..1000.</
               a>. [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 22 2009]
%H A070428 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PerfectPower.html">Perfect Power</a>
%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 Do[ Print[1 + Sum[ -MoebiusMu[x]*Floor[10^(n/x) - 1], {x, 2, 4n}]], {n, 
               0, 24}]
%t A070428 Table[1 - Sum[ MoebiusMu[x]*Floor[10^(n/x) - 1], {x, 2, n*Log[10]/Log[2]}], 
               {n, 0, 24}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 22 2009]
%o A070428 (PARI) for(n=1,18,print(sum(1,x=2,4*n,-mu(x)*(floor(10^(n/x)-1))))
%Y A070428 Cf. A001597.
%Y A070428 Cf. A089579, A089580 (number of perfect powers (not including 1) < 10^n).
%Y A070428 Sequence in context: A149424 A097112 A077284 this_sequence A052529 A049222 
               A001453
%Y A070428 Adjacent sequences: A070425 A070426 A070427 this_sequence A070429 A070430 
               A070431
%K A070428 easy,nonn
%O A070428 0,2
%A A070428 Donald S McDonald (don.mcdonald(AT)paradise.net.nz), 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 (rgwv(AT)rgwv.com), Oct 11 
               2002

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