cp's OEIS Frontend

A081239 #{(i,j): mu(i)*mu(j) = 0, 1<=i,j<=n}, where mu=A008683 (Moebius function).

%I A081239 #11 Jul 13 2013 12:02:57
%S A081239 0,0,0,7,9,11,13,28,45,51,57,80,88,96,104,135,145,180,192,231,245,259,
%T A081239 273,320,369,387,440,495,517,539,561,624,648,672,696,767,793,819,845,
%U A081239 924,952,980,1008,1095,1184,1216,1248,1343,1440,1539,1577,1680,1720
%N A081239 #{(i,j): mu(i)*mu(j) = 0, 1<=i,j<=n}, where mu=A008683 (Moebius function).
%C A081239 A081238(n) + a(n) + A081240(n) = n^2;
%C A081239 a(n) = a(n-1) + 2*n + 1 iff mu(n) = 0.
%H A081239 Reinhard Zumkeller, <a href="/A081239/b081239.txt">Table of n, a(n) for n = 1..500</a>
%F A081239 a(n) = n^2 - A013928(n+1)^2. - _Vladeta Jovovic_, Mar 12 2003
%e A081239 n mu(n) ... n: 1 2 3 4 5 6 7 8
%e A081239 - ------ .... |----------------
%e A081239 1 .. +1 ..... | + - - 0 - + - 0
%e A081239 2 .. -1 ..... | - + + 0 + - + 0
%e A081239 3 .. -1 ..... | - + + 0 + - + 0
%e A081239 4 ... 0 ..... | 0 0 0 0 0 0 0 0
%e A081239 5 .. -1 ..... | - + + 0 + - + 0 a(8)=28, as there are
%e A081239 6 .. +1 ..... | + - - 0 - + - 0 28 '0's in the 8x8-square
%e A081239 7 .. -1 ..... | - + + 0 + - + 0
%e A081239 8 ... 0 ..... | 0 0 0 0 0 0 0 0.
%o A081239 (Haskell)
%o A081239 a081239 n = length [() | u <- [1..n], v <- [1..n],
%o A081239                          a008683 u * a008683 v == 0]
%o A081239 -- _Reinhard Zumkeller_, Aug 03 2012
%Y A081239 Cf. A057627.
%K A081239 nonn
%O A081239 1,4
%A A081239 _Reinhard Zumkeller_, Mar 11 2003