A212819 Numbers up to 10^n with an odd number of prime factors, or negative Liouville function.

0, 5, 51, 507, 5047, 50144, 500265, 5000421, 50001942, 500012608, 5000058013, 50000171112, 500000261313, 5000000483289

Offset

0,2

Links

Table of n, a(n) for n=0..13.

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

Cf. A002819, A008836, A026424, A066829, A090410.

Sequence in context: A342407 A195211 A106415 * A041040 A088320 A223002

Adjacent sequences: A212816 A212817 A212818 * A212820 A212821 A212822

Keyword

nonn

Author

Martin Renner, May 28 2012

Extensions

a(9)-a(13) from Donovan Johnson, May 30 2012

Status

approved