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A077641
Number of squarefree integers in closed interval [n, 2n-1], i.e., among n consecutive numbers beginning with n.
24
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
OFFSET
1,2
FORMULA
a(n) = Sum_{j=0..n-1} abs(mu(n+j)).
a(1) = 1; a(n + 1) = a(n) - issquarefree(n) + issquarefree(2n-2) + issquarefree(2n-1) 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, w-1}]], {w, 1, 128}]
Table[Count[Range[n, 2n-1], _?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, 2i-1}]], {i, nn}]] (* Harvey P. Dale, May 20 2016 *)
CROSSREFS
Cf. A005117.
Sequence in context: A030566 A007963 A137222 * A329547 A330560 A358466
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 14 2002
STATUS
approved