

A077641


Number of squarefree integers in closed interval [n, 2n1], i.e., among n consecutive numbers beginning with n.


2



1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 10, 11, 12, 13, 14, 15, 14, 15, 15, 16, 16, 17, 18, 19, 19, 19, 20, 21, 21, 22, 23, 23, 23, 24, 24, 25, 25, 26, 27, 28, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 37, 38, 38, 39, 38, 39, 40, 41, 41, 41, 42, 43, 43, 44, 45, 45
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..74.


FORMULA

a(n) = Sum_{j=0..n1} abs(mu(n+j)).
a(1) = 1; a(n + 1) = a(n)  issquarefree(n) + issquarefree(2n2) + issquarefree(2n1) for n > 0.  David A. Corneth, May 20 2016


EXAMPLE

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


MATHEMATICA

Table[Apply[Plus, Table[Abs[MoebiusMu[w+j]], {j, 0, w1}]], {w, 1, 128}]
Table[Count[Range[n, 2n1], _?SquareFreeQ], {n, 80}] (* Harvey P. Dale, Oct 27 2013 *)
Module[{nn=80, sf}, sf=Table[If[SquareFreeQ[n], 1, 0], {n, 2nn}]; Table[Total[ Take[ sf, {i, 2i1}]], {i, nn}]] (* Harvey P. Dale, May 20 2016 *)


CROSSREFS

Cf. A005117.
Sequence in context: A030566 A007963 A137222 * A329547 A194210 A112672
Adjacent sequences: A077638 A077639 A077640 * A077642 A077643 A077644


KEYWORD

nonn


AUTHOR

Labos Elemer, Nov 14 2002


STATUS

approved



