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%I M0224 #39 Sep 08 2022 08:44:35
%S 0,1,2,2,2,2,4,4,2,2,4,4,6,4,4,6,8,6,6,6,4,8,8,8,8,8,8,6,10,8,10,10,8,
%T 12,8,10,14,12,10,12,16,10,18,14,12,14,16,14,16,14,10,16,20,14,12,16,
%U 14,20,18,14,22,20,16,20
%N Number of (j,k): j+k=n, (j,n)=(k,n)=1, j,k squarefree.
%C Terms are even or 1: range = A004275. [_Reinhard Zumkeller_, Sep 26 2011]
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Reinhard Zumkeller, <a href="/A007457/b007457.txt">Table of n, a(n) for n = 1..10000</a>
%H Ernesto Bruno Cossi, Joachim Herzog, Paul R. Smith and Richard Stong, <a href="http://www.jstor.org/stable/2324076">Problem 6623</a>, Amer. Math. Monthly, 99 (1992), 573-575.
%H R. G. Wilson v, <a href="/A007376/a007376.pdf">Letter to N. J. A. Sloane, Oct. 1993</a>
%F a(n) = Sum_{i=1..n-1} mu(i*(n-i))^2. - _Ridouane Oudra_, Nov 18 2019
%p with(numtheory): seq(add(mobius(i*(n-i))^2, i=1..n-1), n=1..80); # _Ridouane Oudra_, Nov 18 2019
%t a[n_] := Count[ Table[ If[ SquareFreeQ[j] && GCD[j, n] == 1, If[k = n-j; SquareFreeQ[k] && GCD[k, n] == 1, 1]], {j, 1, n-1}], 1]; Table[a[n], {n, 1, 64}](* _Jean-François Alcover_, Nov 28 2011 *)
%o (Haskell)
%o a007457 n = length [k | k <- [1..n-1], gcd k n == 1, a008966 k == 1,
%o let j = n - k, gcd j n == 1, a008966 j == 1]
%o -- _Reinhard Zumkeller_, Sep 26 2011
%o (Magma) f:=func<i,n|Gcd(i,n) eq 1 and IsSquarefree(i)>; [0] cat [#[i:i in [1..n-1]| f(i,n) and f(n-i,n) ]:n in [2..70]]; // _Marius A. Burtea_, Nov 19 2019
%o (Magma) [0] cat [&+[MoebiusMu(i*(n-i))^2:i in [1..n-1]]:n in [2..70]]; // _Marius A. Burtea_, Nov 19 2019
%Y Cf. A004275, A073311.
%K nonn,nice,easy
%O 1,3
%A _N. J. A. Sloane_, _Robert G. Wilson v_
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