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Number of numbers k<=n with mu(k+n)+mu(k)=0, where mu=A008683 (Moebius function).
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%I #6 Oct 06 2017 20:05:12

%S 1,1,1,3,2,1,3,4,2,3,4,6,5,2,6,9,5,5,7,9,6,7,7,9,6,6,11,14,9,6,10,18,

%T 11,8,10,20,10,12,12,21,12,6,11,25,19,14,11,22,11,16,19,27,12,16,18,

%U 28,15,17,16,23,11,16,26,32,18,16,19,34,21,18,20,43,18,23,31,41,22,16,20,45

%N Number of numbers k<=n with mu(k+n)+mu(k)=0, where mu=A008683 (Moebius function).

%e n=10: mu(1+10)+mu(1)=(-1)+1, mu(5+10)+mu(5)=1+(-1), mu(8+10)+mu(8)=0+0 and mu(k+10)+mu(k)<>0 for k in {2,3,4,6,7,9,10}, therefore a(10)=3.

%t Table[Total[Table[If[MoebiusMu[k+n]+MoebiusMu[n]==0,1,0],{n,k}]],{k,80}] (* _Harvey P. Dale_, Oct 06 2017 *)

%Y Cf. A081247.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Mar 12 2003