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a(n) = +1 if tau(sigma(n)) > tau(n), -1 if n < tau(sigma(n)) < tau(n), and 0 if tau(sigma(n)) = tau(n), where tau = A000005 and sigma = A000203.
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%I #5 Nov 21 2017 21:36:58

%S 0,0,1,-1,1,1,1,0,-1,1,1,0,1,1,1,-1,1,-1,1,1,1,1,1,1,-1,1,1,1,1,1,1,0,

%T 1,1,1,-1,1,1,1,1,1,1,1,1,1,1,1,-1,1,-1,1,0,1,1,1,1,1,1,1,1,1,1,1,-1,

%U 1,1,1,1,1,1,1,-1,1,1,0,1,1,1,1,-1,-1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,-1,1,1,1,1,1

%N a(n) = +1 if tau(sigma(n)) > tau(n), -1 if n < tau(sigma(n)) < tau(n), and 0 if tau(sigma(n)) = tau(n), where tau = A000005 and sigma = A000203.

%H Antti Karttunen, <a href="/A295306/b295306.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = sign(A295305(n)) = sign(A000005(A000203(n)) - A000005(n)).

%o (PARI) A295306(n) = sign(numdiv(sigma(n)) - numdiv(n));

%Y Cf. A000005, A000203, A062068, A295305.

%Y Cf. A037197 (positions of 0'ss), A073803 (of +1's), A073804 (of -1's).

%K sign

%O 1

%A _Antti Karttunen_, Nov 21 2017