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 A143519 A054525 * A010051. 5

%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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