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a(n) = +1 if sigma(phi(n)) > n, -1 if sigma(phi(n)) < n, and 0 if sigma(phi(n)) = n, where phi = A000010 and sigma = A000203.
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%I #9 Feb 07 2025 05:36:24

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

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

%N a(n) = +1 if sigma(phi(n)) > n, -1 if sigma(phi(n)) < n, and 0 if sigma(phi(n)) = n, where phi = A000010 and sigma = A000203.

%H Antti Karttunen, <a href="/A295304/b295304.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = sign(A295302(n)) = sign(sigma(phi(n))-n), where phi = A000010 and sigma = A000203.

%t Array[Sign[DivisorSigma[1, EulerPhi[#]] - #] &, 100] (* _Paolo Xausa_, Feb 07 2025 *)

%o (PARI) A295304(n) = sign(sigma(eulerphi(n)) - n);

%Y Cf. A000010, A000203, A062402, A295302, A295303

%Y Cf. A018784 (positions of 0's), A230201 (of -1's), A230203 (of +1's).

%K sign

%O 1

%A _Antti Karttunen_, Nov 21 2017