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%I
%S 0,1,1,-1,1,-2,1,0,-1,-2,1,1,1,-2,-2,0,1,1,1,1,-2,-2,1,0,-1,-2,0,1,1,
%T 3,1,0,-2,-2,-2,0,1,-2,-2,0,1,3,1,1,1,-2,1,0,-1,1,-2,1,1,0,-2,0,-2,-2,
%U 1,-1,1,-2,1,0,-2,3,1,1,-2,3,1,0,1,-2,1,1,-2,3,1,0,0,-2,1,-1,-2,-2,-2,0,1
%N A054525 * A010051.
%C A010051 = A051731 * A143519 (since A051731 = the inverse Mobius transform).
%F Mobius transform of A010051, the characteristic function of the primes. Row sums of triangle A143518
%e a(4) = -1 since row 4 of triangle A043518 = (0, -1, 0, 0).
%e a(4) = -1 = (0, -1, 0, 1) dot (0, 1, 1, 0), where (0, -1, 0, 1) = row 4 of A054525 and A010051 = (0, 1, 1, 0, 1, 0, 1, 0,...).
%o (Sage)
%o def A143519(n) :
%o D = filter(is_prime, divisors(n))
%o return add(moebius(n/d) for d in D)
%o [A143519(n) for n in (1..89)] # Peter Luschny, Feb 01 2012
%Y Cf. A010051, A143518, A054525, A137851.
%K sign
%O 1,6
%A _Gary W. Adamson_, Aug 22 2008
%E More terms from _R. J. Mathar_, Jan 19 2009
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