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A098235
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Number of ways to write n as a sum of two ordered positive squarefree numbers.
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18
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0, 1, 2, 3, 2, 3, 4, 6, 4, 3, 4, 7, 6, 5, 6, 10, 8, 8, 6, 11, 8, 9, 8, 14, 10, 9, 10, 13, 10, 9, 10, 16, 12, 13, 12, 22, 14, 13, 14, 22, 16, 15, 18, 25, 20, 15, 16, 26, 20, 16, 14, 27, 20, 20, 14, 26, 20, 21, 18, 29, 22, 21, 22, 30, 22, 21, 22, 35, 24, 25, 22, 42, 26, 27, 26, 39
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OFFSET
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1,3
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COMMENTS
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a(n) ~ n * Prod[p prime, (1-2/p^2) * Prod[p^2|n, (p^2-1)/(p^2-2)]].
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n-1} (mu(k)*mu(n-k))^2. - Benoit Cloitre, Sep 24 2006
G.f.: ( Sum_{k>=1} mu(k)^2*x^k )^2, where mu(k) is the Moebius function (A008683). - Ilya Gutkovskiy, Dec 28 2016
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EXAMPLE
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a(12)=7 because 12=1+11=2+10=5+7=6+6=7+5=10+2=11+1.
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MATHEMATICA
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Join[{0}, Table[Sum[(MoebiusMu[k]*MoebiusMu[n - k + 1])^2, {k, 1, n}], {n, 1, 50}]] (* G. C. Greubel, Dec 28 2016 *)
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PROG
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(PARI) a(n) = sum(k=1, n-1, (moebius(k)*moebius(n-k))^2) \\ Indranil Ghosh, Mar 10 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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