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%I #14 May 30 2012 16:42:55
%S 0,5,51,507,5047,50144,500265,5000421,50001942,500012608,5000058013,
%T 50000171112,500000261313,5000000483289
%N Numbers up to 10^n with an odd number of prime factors, or negative Liouville function.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LiouvilleFunction.html">Liouville Function</a>
%F a(n) = A011557(n) - A212818(n).
%F a(n) = (10^n)/2 - A090410(n)/2. - _Donovan Johnson_, May 30 2012
%F a(n) = A055038(10^n). - _Ray Chandler_, May 30 2012
%e a(1) = 5 since up to 10 there are the five numbers 2, 3, 5, 7, 8 with an odd number of prime factors or negative Liouville function.
%p zg:=0: zu:=0: G:=[]: U:=[]: k:=0:
%p for i from 1 to 10^8 do if numtheory[bigomega](i) mod 2 = 0 then zg:=zg+1: else zu:=zu+1: fi: if i=10^k then G:=[op(G),zg]: U:=[op(U),zu]: k:=k+1: fi: od:
%p print(U);
%t Table[Count[LiouvilleLambda[Range[10^n]], -1], {n, 0, 5}] (* _Ray Chandler_, May 30 2012 *)
%Y Cf. A002819, A008836, A026424, A066829, A090410.
%K nonn
%O 0,2
%A _Martin Renner_, May 28 2012
%E a(9)-a(13) from _Donovan Johnson_, May 30 2012
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