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A077643
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Number of squarefree integers in closed interval [2^n, -1 + 2*2^n], i.e., among 2^n consecutive numbers beginning with 2^n.
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1
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1, 2, 3, 5, 9, 19, 39, 79, 157, 310, 621, 1246, 2491, 4980, 9958, 19924, 39844, 79672, 159365, 318736, 637457, 1274916, 2549816, 5099651, 10199363, 20398663, 40797299, 81594571, 163189087, 326378438, 652756861, 1305513511, 2611026987
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{j=0..-1+2^n} abs(mu(2^n + j)).
a(n)/2^n approaches 1/Zeta(2), so limiting sequence is floor(2^n/Zeta(2)), n >= 0. - Wouter Meeussen, May 25 2003
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EXAMPLE
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n=4: among 16 numbers of {16,...,31}, nine are squarefree [17,19,21,22,23,26,29,30,31], so a(4)=9.
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MATHEMATICA
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Table[Apply[Plus, Table[Abs[MoebiusMu[2^w+j]], {j, 0, 2^w-1}]], {w, 0, 15}]
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PROG
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(PARI) { a(n) = sum(m=1, sqrtint(2^(n+1)-1), moebius(m) * ((2^(n+1)-1)\m^2 - (2^n-1)\m^2) ) } \\ Max Alekseyev, Oct 18 2008
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 12 2003
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STATUS
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approved
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