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A319210 a(n) = phi(n^2 - 1)/2 where phi is A000010.

%I A319210 #27 Dec 09 2024 05:28:36
%S A319210 1,2,4,4,12,8,18,16,30,16,60,24,48,48,64,48,144,48,108,80,132,80,220,
%T A319210 96,180,144,252,96,420,128,300,256,240,192,432,216,432,288,480,192,
%U A319210 840,240,504,440,552,352,966,320,672,480,832,432,1040,432,720,672,1044,448
%N A319210 a(n) = phi(n^2 - 1)/2 where phi is A000010.
%H A319210 Seiichi Manyama, <a href="/A319210/b319210.txt">Table of n, a(n) for n = 2..1000</a>
%H A319210 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%H A319210 Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's totient function</a>.
%F A319210 Sum_{k=1..n} a(k) = c * n^3 / 4 + O((n*log(n))^2), where c = Product_{p prime} (1 - 2/p^2) = 0.322634... (A065474). - _Amiram Eldar_, Dec 09 2024
%t A319210 Table[(EulerPhi@(n^2 - 1) / 2), {n, 2, 70}] (* _Vincenzo Librandi_, Sep 15 2018 *)
%o A319210 (PARI) {a(n) = eulerphi(n^2-1)/2}
%o A319210 (Magma) [EulerPhi(n^2-1)/2: n in [2..70]]; // _Vincenzo Librandi_, Sep 15 2018
%Y A319210 Row 2 of A369291.
%Y A319210 Cf. A000010, A005563 (n^2-1, shifted), A065474.
%Y A319210 phi(n^b - 1)/b: this sequence (b=2), A319213 (b=3), A319214 (b=5).
%K A319210 nonn,easy
%O A319210 2,2
%A A319210 _Seiichi Manyama_, Sep 13 2018