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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=Sum[Abs(mu[2^n+j]); j=0...-1+2^n)]
a(n)/2^n approaches 1/Zeta[2], so limiting sequence is Table[Floor[2^n/Zeta[2]], {n, 0, 36}] - Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 25 2003
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EXAMPLE
| 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
| Table[Apply[Plus, Table[Abs[MoebiusMu[2^w+j]], {j, 0, 2^w-1}]], {w, 0, 15}]
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PROG
| (PARI) { a(n) = sum(m=1, sqrtint(2^(n+1)-1), moebius(m) * ((2^(n+1)-1)\m^2 - (2^n-1)\m^2) ) } [From Max Alekseyev (maxale(AT)gmail.com), Oct 18 2008]
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CROSSREFS
| Cf. A077641, A077642.
Sequence in context: A003218 A058770 A049910 * A123389 A113984 A110542
Adjacent sequences: A077640 A077641 A077642 * A077644 A077645 A077646
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Nov 14 2002
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EXTENSIONS
| More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 12 2003
More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 25 2003
a(25) and up from Max Alekseyev (maxale(AT)gmail.com), Oct 18 2008
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