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%I #30 Mar 12 2018 03:49:47
%S 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,
%T 10,16,12,13,12,22,14,13,14,22,16,15,18,25,20,15,16,26,20,16,14,27,20,
%U 20,14,26,20,21,18,29,22,21,22,30,22,21,22,35,24,25,22,42,26,27,26,39
%N Number of ways to write n as a sum of two ordered positive squarefree numbers.
%C a(n) ~ n * Prod[p prime, (1-2/p^2) * Prod[p^2|n, (p^2-1)/(p^2-2)]].
%H T. D. Noe, <a href="/A098235/b098235.txt">Table of n, a(n) for n = 1..10000</a>
%H P. Pollack, <a href="http://www.math.dartmouth.edu/~ppollack/notes.pdf">Analytic and Combinatorial Number Theory</a>, Course Notes, p. 122, 202. [?Broken link]
%H P. Pollack, <a href="http://alpha01.dm.unito.it/personalpages/cerruti/ac/notes.pdf">Analytic and Combinatorial Number Theory</a>, Course Notes, p. 122, 202.
%F a(n) = Sum_{k=1..n-1} (mu(k)*mu(n-k))^2. - _Benoit Cloitre_, Sep 24 2006
%F a(n) = Sum_{k=1..n-1} ( A008966(k)*A008966(n-k) ). - _Reinhard Zumkeller_, Nov 04 2009
%F G.f.: ( Sum_{k>=1} mu(k)^2*x^k )^2, where mu(k) is the Moebius function (A008683). - _Ilya Gutkovskiy_, Dec 28 2016
%e a(12)=7 because 12=1+11=2+10=5+7=6+6=7+5=10+2=11+1.
%t Join[{0}, Table[Sum[(MoebiusMu[k]*MoebiusMu[n - k + 1])^2, {k, 1, n}], {n, 1, 50}]] (* _G. C. Greubel_, Dec 28 2016 *)
%o (PARI) a(n) = sum(k=1, n-1, (moebius(k)*moebius(n-k))^2) \\ _Indranil Ghosh_, Mar 10 2017
%o (PARI) a(n)=my(s); forsquarefree(k=1, n-1, s+=issquarefree(n-k)); s \\ _Charles R Greathouse IV_, Jan 08 2018
%Y Cf. A005117, A098236, A071068.
%K nonn
%O 1,3
%A _Ralf Stephan_, Aug 31 2004
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