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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 (list; graph; refs; listen; history; text; internal format)
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 * A088320 A041040 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

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)