A070544 Number of squarefree numbers s such that n < s < 2n.
0, 1, 1, 3, 2, 3, 3, 5, 6, 6, 6, 8, 7, 7, 7, 9, 9, 11, 11, 13, 13, 14, 13, 15, 15, 15, 16, 17, 17, 18, 18, 19, 19, 20, 20, 22, 22, 22, 22, 24, 23, 24, 24, 26, 27, 27, 27, 29, 30, 30, 30, 32, 32, 34, 34, 36, 36, 37, 36, 38, 37, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 44, 44, 44, 45
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[Count[Range[n+1,2n-1],?SquareFreeQ],{n,80}] (* _Harvey P. Dale, Mar 23 2019 *)
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PARI
a(n) = sum(i=n+1,2*n-1,issquarefree(i));
Formula
Limit_{n -> oo} a(n)/n = 6/Pi^2 (A059956).
From Wesley Ivan Hurt, Jan 08 2022: (Start)
a(n) = Sum_{k=1..n-1} mu(2n-k)^2.
a(n) = Sum_{k=n+1..2n-1} mu(k)^2.
a(n) = Sum_{k=(n^2-n+2)/2..(n^2+n-2)/2} mu(A128076(k))^2. (End)