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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
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
Sequence in context: A119002 A058770 A049910 * A123389 A113984 A110542
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 March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)