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 A081238 #{(i,j): mu(i)*mu(j) = -1, 1 <= i <= n, 1 <= j <= n}, where mu=A008683 (Moebius function). 3
 0, 2, 4, 4, 6, 12, 16, 16, 16, 24, 30, 30, 36, 48, 60, 60, 70, 70, 80, 80, 96, 112, 126, 126, 126, 144, 144, 144, 160, 176, 192, 192, 216, 240, 264, 264, 286, 312, 338, 338, 364, 390, 416, 416, 416, 448, 476, 476, 476, 476, 510, 510, 540, 540, 576, 576, 612, 648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..500 FORMULA a(n) + A081239(n) + A081240(n) = n^2; a(n) = a(n-1) iff mu(n) = 0. a(n) = 2*A070548(n)*A070549(n). - Robert Israel, Jan 08 2018 EXAMPLE n mu(n) n: 1 2 3 4 5 6 7 8 - ----- +-----------------> 1 +1 | + - - 0 - + - 0 2 -1 | - + + 0 + - + 0 3 -1 | - + + 0 + - + 0 4 0 | 0 0 0 0 0 0 0 0 5 -1 | - + + 0 + - + 0 a(8)=16, as there are 6 +1 | + - - 0 - + - 0 16 '-1's in the 8 X 8 square 7 -1 | - + + 0 + - + 0 (represented as '-') 8 0 | 0 0 0 0 0 0 0 0 MAPLE Nplus:= 0: Nminus:=0: for n from 1 to 100 do v:= numtheory:-mobius(n); if v = 1 then Nplus:= Nplus+1 elif v = -1 then Nminus:= Nminus+1 fi; A[n]:= 2*Nplus*Nminus; od: seq(A[n], n=1..100); # Robert Israel, Jan 08 2018 MATHEMATICA Nplus = Nminus = 0; For[n = 1, n <= 100, n++, v = MoebiusMu[n]; If[v == 1, Nplus++, If[v == -1, Nminus++]]; a[n] = 2 Nplus Nminus]; Array[a, 100] (* Jean-François Alcover, Dec 16 2021, after Robert Israel *) PROG (Haskell) a081238 n = length [() | u <- [1..n], v <- [1..n], a008683 u * a008683 v == -1] -- Reinhard Zumkeller, Aug 03 2012 CROSSREFS Cf. A070548, A070549, A081239, A081240. Sequence in context: A224487 A185342 A276985 * A333823 A207254 A207403 Adjacent sequences: A081235 A081236 A081237 * A081239 A081240 A081241 KEYWORD nonn AUTHOR Reinhard Zumkeller, Mar 11 2003 STATUS approved

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Last modified June 1 17:57 EDT 2023. Contains 363076 sequences. (Running on oeis4.)