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A212819
Numbers up to 10^n with an odd number of prime factors, or negative Liouville function.
1
0, 5, 51, 507, 5047, 50144, 500265, 5000421, 50001942, 500012608, 5000058013, 50000171112, 500000261313, 5000000483289
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Liouville Function
FORMULA
a(n) = A011557(n) - A212818(n).
a(n) = (10^n)/2 - A090410(n)/2. - Donovan Johnson, May 30 2012
a(n) = A055038(10^n). - Ray Chandler, May 30 2012
EXAMPLE
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.
MAPLE
zg:=0: zu:=0: G:=[]: U:=[]: k:=0:
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:
print(U);
MATHEMATICA
Table[Count[LiouvilleLambda[Range[10^n]], -1], {n, 0, 5}] (* Ray Chandler, May 30 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Martin Renner, May 28 2012
EXTENSIONS
a(9)-a(13) from Donovan Johnson, May 30 2012
STATUS
approved