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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
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; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..32.

FORMULA

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

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.

MATHEMATICA

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

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) ) } \\ Max Alekseyev, Oct 18 2008

CROSSREFS

Cf. A077641, A077642.

Sequence in context: A119002 A058770 A049910 * A123389 A113984 A110542

Adjacent sequences:  A077640 A077641 A077642 * A077644 A077645 A077646

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 14 2002

EXTENSIONS

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

More terms from Wouter Meeussen, May 25 2003

a(25) and up from Max Alekseyev, Oct 18 2008

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)