A160115 - OEIS

%I #8 Aug 08 2024 11:07:33

%S 0,0,1,0,1,0,1,1,1,1,2,2,3,0,-1,-1,1,2,0,-1,0,2,6,1,2,7,5,-1,-7,-4,4,

%T -7,-21,-7,-2,30,2,14,-8,7,-1,-7,-12,-1,21,28,7,-29,-33,-76,-88,15,47,

%U 58,-51,-112,293,122,316,-96,-42,-259,140,-111,6,-790,-342,146,395,1087

%N Fluctuations of the number of cubefree integers not exceeding 2^n

%C The asymptotic density of cubefree integers is the reciprocal of Apery's constant 1/zeta(3) = 0.83190737258... The number of cubefree integers not exceeding N is thus roughly N/zeta(3). When N is a power of 2, this sequence gives the difference between the actual number (A160113) and that linear estimate (rounded to the nearest integer).

%H Chai Wah Wu, <a href="/A160115/b160115.txt">Table of n, a(n) for n = 0..99</a>

%H G. P. Michon, <a href="http://www.numericana.com/answer/constants.htm#apery">Reciprocal of Apery's constant</a>.

%H G. P. Michon, <a href="http://www.numericana.com/answer/counting.htm#cubefree">On the number of cubefree integers not exceeding N</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cubefree.html">Cubefree</a>.

%F a(n) = A160113(n)-round(2^n/zeta(3))

%Y A004709 (cubefree integers). A160112 & A160113 (counting cubefree integers).

%K easy,sign

%O 0,11

%A _Gerard P. Michon_, May 06 2009