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A228498 a(n) = sigma(n^2) + phi(n^2) - 2n^2.

%I A228498 #31 Dec 03 2023 05:02:04
%S A228498 0,1,1,7,1,31,1,31,13,57,1,163,1,91,73,127,1,307,1,321,111,183,1,691,
%T A228498 31,241,121,535,1,1261,1,511,211,381,157,1591,1,463,273,1377,1,2163,1,
%U A228498 1131,781,651,1,2803,57,1467,421,1513,1,2791,273,2311,507,993,1,6253,1,1123,1227,2047,343,4711,1,2445,703
%N A228498 a(n) = sigma(n^2) + phi(n^2) - 2n^2.
%C A228498 If n is a prime, p, then a(p) = 1. Proof: a(p) = sigma(p^2) + phi(p^2) - 2p^2 = p^2 + p + 1 + p^2*( 1-(1/p) ) - 2p^2 = p^2 + p + 1 + p^2 - p - 2p^2 = 1.
%H A228498 Antti Karttunen, <a href="/A228498/b228498.txt">Table of n, a(n) for n = 1..16384</a>
%F A228498 a(n) = A051709(n^2).
%F A228498 a(n) = A000203(n^2) + A000010(n^2) - 2*n^2.
%F A228498 a(n) = A065764(n) + A002618(n) - A001105(n).
%F A228498 Sum_{k=1..n} a(k) ~ ((5*zeta(3) + 2)/ Pi^2 - 2/3) * n^3. - _Amiram Eldar_, Dec 03 2023
%e A228498 a(6) = 31; sigma(6^2) + phi(6^2) - 2*6^2 = 91 + 12 - 72 = 31.
%p A228498 with(numtheory); seq(sigma(k^2) + phi(k^2) - 2*k^2, k=1..20);
%t A228498 Table[DivisorSigma[1, n^2] + EulerPhi[n^2] - 2*n^2, {n, 100}]
%o A228498 (PARI) vector(100, n, sigma(n^2)+eulerphi(n^2)-2*n^2) \\ _Altug Alkan_, Oct 28 2015
%Y A228498 Cf. A051709 (sequence at n instead of n^2).
%Y A228498 Cf. A000010, A000203, A001105, A002117, A002618, A065764.
%K A228498 nonn,easy
%O A228498 1,4
%A A228498 _Wesley Ivan Hurt_, Aug 23 2013
%E A228498 More terms from _Antti Karttunen_, Oct 30 2017