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A256942
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Number of odd squarefree numbers <= 2^n.
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0
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1, 1, 2, 4, 7, 13, 26, 52, 105, 209, 415, 830, 1661, 3321, 6641, 13279, 26565, 53123, 106237, 212488, 424973, 849945, 1699889, 3399761, 6799540, 13599124, 27198203, 54396423, 108792774, 217585510, 435171212, 870342371, 1740684723
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OFFSET
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0,3
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COMMENTS
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a(n) + a(n+1) = A143658(n+1).
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LINKS
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Table of n, a(n) for n=0..32.
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FORMULA
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a(n) = sum(j=0..n, (-1)^j*A143658(n-j)).
a(n) = 2/3 * A143658(n) + 1/3 * sum(i=1..floor(2^(n/2)), A008683(i)*A065359(floor(2^n/i^2))).
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EXAMPLE
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For n=4 there are 7 odd squarefree numbers <= 2^4, namely 1,3,5,7,11,13,15.
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MAPLE
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g:= proc(n) option remember; local L ; L := convert(n, base, 2) ; (2*n - add( L[i]*(-1)^i, i=1..nops(L)))/3 ; end proc:
a:= n -> add(numtheory:-mobius(i)*g(floor(2^n/i^2)), i=1..floor(2^(n/2))):
seq(a(n), n=0..32);
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CROSSREFS
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Cf. A008683, A065359, A143658.
Sequence in context: A293314 A023431 A025246 * A112740 A309050 A265580
Adjacent sequences: A256939 A256940 A256941 * A256943 A256944 A256945
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KEYWORD
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nonn
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AUTHOR
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Robert Israel, Apr 13 2015
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STATUS
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approved
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