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A265675 Number of smaller squarefree numbers that are coprime to the n-th squarefree number.

%I A265675 #16 Oct 12 2024 18:58:13
%S A265675 0,1,2,3,2,5,3,7,8,5,6,11,12,8,9,15,10,17,8,19,13,13,15,23,15,17,26,
%T A265675 11,28,18,30,21,32,25,23,23,36,37,25,30,18,41,29,22,44,45,30,36,22,49,
%U A265675 32,51,41,34,39,55,44,41,38,47,60,61,30,63,36,43,66,67
%N A265675 Number of smaller squarefree numbers that are coprime to the n-th squarefree number.
%C A265675 a(n) = number of A005117(k) such that A005117(k) and A005117(n) are coprime, k = 1..n-1.
%H A265675 Reinhard Zumkeller, <a href="/A265675/b265675.txt">Table of n, a(n) for n = 1..10000</a>
%F A265675 a(n) = Sum_{k=1..n-1} A008966(A005117(n)*A005117(k)).
%e A265675 A005117(7) = 10, A005117(1..6) = [1,2,3,5,6,7],
%e A265675 ->  a(7) = #{1,3,7} = 3;
%e A265675 A005117(8) = 11, A005117(1..7) = [1,2,3,5,6,7,10],
%e A265675 ->  a(8) = #{1,2,3,5,6,7,10} = 7;
%e A265675 A005117(9) = 13, A005117(1..8) = [1,2,3,5,6,7,10,11],
%e A265675 ->  a(9) = #{1,2,3,5,6,7,10,11} = 8;
%e A265675 A005117(10) = 14, A005117(1..9) = [1,2,3,5,6,7,10,11,13],
%e A265675 ->  a(10) = #{1,3,5,11,13} = 5;
%e A265675 A005117(11) = 15, A005117(1..10) = [1,2,3,5,6,7,10,11,13,14],
%e A265675 ->  a(11) = #{1,2,7,11,13,14} = 6.
%t A265675 With[{sf=Select[Range[200],SquareFreeQ]},Table[Total[Boole[CoprimeQ[sf[[n]],sf[[Range[1,n-1]]]]]],{n,70}]] (* _Harvey P. Dale_, Oct 12 2024 *)
%o A265675 (Haskell)
%o A265675 import Data.List (inits)
%o A265675 a265675 n = a265675_list !! (n-1)
%o A265675 a265675_list = map (\(x:xs) -> length $ filter ((== 1) . gcd x) xs) $
%o A265675                    map reverse $ tail $ inits a005117_list
%Y A265675 Cf. A005117, A008966.
%K A265675 nonn
%O A265675 1,3
%A A265675 _Reinhard Zumkeller_, Dec 13 2015