This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A169646 #24 May 12 2025 08:30:02
%S A169646 1,1,2,0,3,2,5,0,0,3,7,0,8,5,6,0,11,0,12,0,8,9,15,0,0,10,0,0,17,8,19,
%T A169646 0,13,13,15,0,23,15,17,0,26,11,28,0,0,18,30,0,0,0,21,0,32,0,25,0,23,
%U A169646 23,36,0,37,25,0,0,30,18,41,0,29,22,44,0,45,30,0,0,36,22,49,0,0,32,51,0,41,34
%N A169646 Number of squarefree numbers of form k*n, 1 <= k <= n.
%H A169646 Vincenzo Librandi, <a href="/A169646/b169646.txt">Table of n, a(n) for n = 1..3000</a>
%F A169646 a(n) = A008966(n)*A073311(n).
%F A169646 a(A000040(n)) = A112929(n).
%F A169646 a(n) = Sum_{i=1..n} A008966(n*i). - _Ridouane Oudra_, Jul 24 2019
%F A169646 a(n) = (A118259(n) - A118259(n-1))/2, for n>1. - _Ridouane Oudra_, May 04 2025
%F A169646 Sum_{k=1..n} a(k) ~ c * n / 2, where c = Product_{p prime} (1 - (3*p-2)/(p^3)) (A065473). - _Amiram Eldar_, May 12 2025
%p A169646 with(numtheory): seq(add(mobius(n*i)^2, i = 1 .. n), n = 1 .. 90); # _Ridouane Oudra_, Jul 24 2019
%t A169646 Count[#,_?SquareFreeQ]&/@Table[k*n,{n,90},{k,n}] (* _Harvey P. Dale_, Sep 05 2012 *)
%t A169646 Table[Sum[MoebiusMu[i n]^2, {i, n}], {n, 100}] (* _Vincenzo Librandi_, Jul 25 2019 *)
%o A169646 (Magma) [&+[MoebiusMu(k*n)^2: k in [1..n]]: n in [1..80]]; // _Vincenzo Librandi_, Jul 25 2019
%o A169646 (PARI) a(n) = sum(i = 1, n, issquarefree(i*n)); \\ _Amiram Eldar_, May 12 2025
%Y A169646 Cf. A000040, A008966, A065473, A073311, A112929, A118259.
%K A169646 nonn
%O A169646 1,3
%A A169646 _Reinhard Zumkeller_, Apr 05 2010