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A077643 Number of squarefree integers in closed interval [2^n, -1 + 2*2^n], i.e., among 2^n consecutive numbers beginning with 2^n. 1

%I

%S 1,2,3,5,9,19,39,79,157,310,621,1246,2491,4980,9958,19924,39844,79672,

%T 159365,318736,637457,1274916,2549816,5099651,10199363,20398663,

%U 40797299,81594571,163189087,326378438,652756861,1305513511,2611026987

%N Number of squarefree integers in closed interval [2^n, -1 + 2*2^n], i.e., among 2^n consecutive numbers beginning with 2^n.

%F a(n) = Sum_{j=0..-1+2^n} abs(mu(2^n + j)).

%F a(n)/2^n approaches 1/Zeta(2), so limiting sequence is floor(2^n/Zeta(2)), n >= 0. - _Wouter Meeussen_, May 25 2003

%e n=4: among 16 numbers of {16,...,31}, nine are squarefree [17,19,21,22,23,26,29,30,31], so a(4)=9.

%t Table[Apply[Plus, Table[Abs[MoebiusMu[2^w+j]], {j, 0, 2^w-1}]], {w, 0, 15}]

%o (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

%Y Cf. A077641, A077642.

%K nonn

%O 0,2

%A _Labos Elemer_, Nov 14 2002

%E More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 12 2003

%E More terms from _Wouter Meeussen_, May 25 2003

%E a(25) and up from _Max Alekseyev_, Oct 18 2008

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Last modified November 22 16:31 EST 2019. Contains 329396 sequences. (Running on oeis4.)