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A077642 Number of squarefree integers in the closed interval [10^n, -1 + 2*10^n], i.e., among 10^n consecutive integers beginning with 10^n. 1
1, 7, 61, 607, 6077, 60787, 607951, 6079284, 60792732, 607927092, 6079270913, 60792710227, 607927101577, 6079271018873, 60792710185938, 607927101853650 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

What a(n)/n is converging to?

lim_{n->inf} a(n)/10^n = 1/zeta(2). [Max Alekseyev, Oct 18 2008]

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) = Sum_{j=0..-1+10^n} abs(mu(10^n + j)).

EXAMPLE

n=10: among numbers {10,...,19} seven are squarefree [10,11,13,14,15,17,19], so a(1)=7.

MAPLE

with(numtheory): for n from 0 to 5 do ct:=0: for k from 10^n to 2*10^n-1 do if abs(mobius(k))>0 then ct:=ct+1 else ct:=ct: fi: od: a[n]:=ct: od: seq(a[n], n=0..5); # Emeric Deutsch, Mar 28 2005

MATHEMATICA

Table[Apply[Plus, Table[Abs[MoebiusMu[10^w+j]], {j, 0, -1+10^(w-1)}]], {w, 0, 6}]

PROG

(PARI) { a(n) = sum(m=1, sqrtint(2*10^n-1), moebius(m) * ((2*10^n-1)\m^2 - (10^n-1)\m^2) ) } \\ Max Alekseyev, Oct 18 2008

CROSSREFS

Cf. A077641, A077643.

Sequence in context: A199686 A113718 A177132 * A071172 A259335 A127688

Adjacent sequences:  A077639 A077640 A077641 * A077643 A077644 A077645

KEYWORD

more,nonn

AUTHOR

Labos Elemer, Nov 14 2002

EXTENSIONS

6079284 from Emeric Deutsch, Mar 28 2005

a(8)-a(15) from Max Alekseyev, Oct 18 2008

STATUS

approved

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Last modified February 28 08:28 EST 2020. Contains 332323 sequences. (Running on oeis4.)