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%I #5 Apr 05 2012 17:23:14
%S 1,1,2,0,4,-3,6,0,0,-5,10,0,12,-7,-6,0,16,0,18,0,-8,-11,22,0,0,-13,0,
%T 0,28,7,30,0,-12,-17,-10,0,36,-19,-14,0,40,9,42,0,0,-23,46,0,0,0,-18,
%U 0,52,0,-14,0,-20,-29,58,0,60,-31,0,0,-16,13,66,0,-24,11,70,0,72,-37,0,0,-16
%N Mobius transform of A014963.
%C Conjectures relating to the Mobius sequence A008683:
%C If mu(n) = 0, a(n) = 0.
%C If mu(n) = 1, (n>1), a(n) = a negative term.
%C If mu(n) = -1, a(n) = a positive term.
%C So except for the first term and zero divided by zero we would have mu(n) = -a(n)/abs(a(n)).
%C Examples: mu(4) = 0, a(4) = 0; mu(6) = 1, a(6) = (-3); mu(7) = (-1), a(7) = 6.
%H Physics Forums discussion, <a href="http://www.physicsforums.com/showthread.php?t=35060">Moebius function</a>.
%H Eric. W. Weisstein, <a href="http://mathworld.wolfram.com/MertensConjecture.html">Mertens Conjecture</a>.
%F A054525 as an infinite lower triangular matrix * A014963 as a vector.
%e a(5) = -3 = (1, -1, -1, 0, 0, 1) dot (1, 2, 3, 2, 5, 1) = (1 - 2 - 3 + 0 + 0 + 1), where (1, -1, -1, 0, 0, 1) = row 5 of triangle A054525 and (1, 2, 3, 2, 5, 1) = the first 5 terms of A014963.
%Y Cf. A014963, A008683, A140255, A140256.
%K sign
%O 1,3
%A _Gary W. Adamson_ and _Mats Granvik_, May 16 2008, Jun 29 2008
%E More terms from _Mats Granvik_, Jun 29 2008
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