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A247418
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a(n) = Sum_{i=1..n} mu(i)*(-1)^(i+1).
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2
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1, 2, 1, 1, 0, -1, -2, -2, -2, -3, -4, -4, -5, -6, -5, -5, -6, -6, -7, -7, -6, -7, -8, -8, -8, -9, -9, -9, -10, -9, -10, -10, -9, -10, -9, -9, -10, -11, -10, -10, -11, -10, -11, -11, -11, -12, -13, -13, -13, -13, -12, -12, -13, -13, -12, -12, -11, -12, -13
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OFFSET
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1,2
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COMMENTS
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Alternating sums of mu(n), the Moebius function (A008683), from 1 to n.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} A008683(i)*(-1)^(i+1).
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EXAMPLE
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a(n) = mu(1) - mu(2) + mu(3) - mu(4) + ... + (-1)^(n+1) * mu(n).
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MAPLE
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with(numtheory): A247418:=n->add(mobius(i)*(-1)^(i+1), i=1..n): seq(A247418(n), n=1..50);
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MATHEMATICA
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Table[Sum[MoebiusMu[i] (-1)^(i + 1), {i, n}], {n, 50}]
Accumulate[Table[MoebiusMu[n](-1)^(n+1), {n, 60}]] (* Harvey P. Dale, Oct 19 2018 *)
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PROG
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(PARI) a(n) = sum(i=1, n, moebius(i)*(-1)^(i+1)); \\ Michel Marcus, Sep 18 2014
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CROSSREFS
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Cf. A068773 (alternating sums of eulerphi(n)).
Cf. A068762 (alternating sums of sigma(n)).
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KEYWORD
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AUTHOR
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STATUS
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approved
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