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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
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
Ernesto Bruno Cossi, Joachim Herzog, Paul R. Smith and Richard Stong, Problem 6623, Amer. Math. Monthly, 99 (1992), 573-575.
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<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
(Magma) [0] cat [&+[MoebiusMu(i*(n-i))^2:i in [1..n-1]]:n in [2..70]]; // Marius A. Burtea, Nov 19 2019
CROSSREFS
Sequence in context: A151565 A060632 A160407 * A119802 A237120 A060369
KEYWORD
nonn,nice,easy
STATUS
approved