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 A007457 Number of (j,k): j+k=n, (j,n)=(k,n)=1, j,k squarefree. (Formerly M0224) 2
 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, 12, 8, 10, 14, 12, 10, 12, 16, 10, 18, 14, 12, 14, 16, 14, 16, 14, 10, 16, 20, 14, 12, 16, 14, 20, 18, 14, 22, 20, 16, 20 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Terms are even or 1: range = A004275. [Reinhard Zumkeller, Sep 26 2011] REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Ernesto Bruno Cossi, Joachim Herzog, Paul R. Smith and Richard Stong, Problem 6623, Amer. Math. Monthly, 99 (1992), 573-575. R. G. Wilson v, Letter to N. J. A. Sloane, Oct. 1993 FORMULA a(n) = Sum_{i=1..n-1} mu(i*(n-i))^2. - Ridouane Oudra, Nov 18 2019 MAPLE with(numtheory): seq(add(mobius(i*(n-i))^2, i=1..n-1), n=1..80); # Ridouane Oudra, Nov 18 2019 MATHEMATICA 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 *) PROG (Haskell) a007457 n = length [k | k <- [1..n-1], gcd k n == 1, a008966 k == 1,                         let j = n - k, gcd j n == 1, a008966 j == 1] -- Reinhard Zumkeller, Sep 26 2011 (MAGMA) f:=func; [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 (MAGMA) [0] cat [&+[MoebiusMu(i*(n-i))^2:i in [1..n-1]]:n in [2..70]]; // Marius A. Burtea, Nov 19 2019 CROSSREFS Cf. A004275, A073311. Sequence in context: A151565 A060632 A160407 * A119802 A237120 A060369 Adjacent sequences:  A007454 A007455 A007456 * A007458 A007459 A007460 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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Last modified April 9 12:51 EDT 2020. Contains 333352 sequences. (Running on oeis4.)