Search: id:A160112
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%I A160112
%S A160112 1,9,85,833,8319,83190,831910,8319081,83190727,831907372,8319073719,
%T A160112 83190737244,831907372522,8319073725828,83190737258105,831907372580692,
%U A160112 8319073725807178,83190737258070643,831907372580707771
%N A160112 Number of cubefree integers not exceeding 10^n.
%C A160112 An alternate definition specifying "less than 10^n" would yield the same 
               sequence except for the first 3 terms: 0, 8, 84, 833, 8319, etc. 
               (since powers of 10 beyond 1000 are not cubefree anyhow).
%C A160112 The limit of a(n)/10^n is the inverse of Apery's constant, 1/zeta(3), 
               whose digits are given by A088453.
%H A160112 G. P. Michon, <a href="b160112.txt">Table of n, a(n) for = n=0..29</a>
%H A160112 G. P. Michon, <a href="http://www.numericana.com/answer/counting.htm#cubefree">
               On the number of cubefree integers not exceeding N</a>.
%F A160112 a(n) = Sum for i=1 to 10^(n/3) of A008683(i)*floor(10^n/i^3)
%e A160112 a(0)=1 because 1 <= 10^0 is not a multiple of the cube of a prime.
%e A160112 a(1)=9 because the 9 numbers 1,2,3,4,5,6,7,9,10 are cubefree; 8 is not.
%e A160112 a(2)=85 because there are 85 cubefree integers equal to 100 or less.
%e A160112 a(3)=833 because there are 833 cubefree integers below 1000 (which is 
               not cube-free itself).
%t A160112 Table[ Sum[ MoebiusMu[x]*Floor[10^n/(x^3)], {x, 10^(n/3)}], {n, 0, 18}] 
               [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 27 2009]
%Y A160112 A004709 (cube-free numbers). A088453 (limit of the string of digits). 
               A160113 (binary counterpart for cubefree integers). A071172 & A053462 
               (decimal counterpart for squarefree integers). A143658 (binary counterpart 
               for squarefree integers).
%Y A160112 Sequence in context: A024118 A015580 A163308 this_sequence A108427 A152106 
               A142982
%Y A160112 Adjacent sequences: A160109 A160110 A160111 this_sequence A160113 A160114 
               A160115
%K A160112 easy,nice,nonn
%O A160112 0,2
%A A160112 Gerard P. Michon (g.michon(AT)att.net), May 02 2009, May 06 2009

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