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%I #24 Dec 21 2023 01:15:16
%S 0,1,2,4,4,8,6,16,18,24,10,32,12,48,56,64,16,72,18,96,108,120,22,128,
%T 100,168,162,192,28,176,30,256,260,288,264,288,36,360,360,384,40,360,
%U 42,480,504,528,46,512,294,600,608,672,52,648,600,768,756,840,58,704,60
%N a(n) = phi(n)*(n - phi(n)).
%H C. A. Nicol, <a href="https://doi.org/10.1073/pnas.40.5.363">On restricted partitions and a generalization of the Euler phi number and the Moebius function</a>, PNAS September 1, 1953 vol. 39 no. 9 963-968.
%F For n > 1, a(n) = Sum_{k=1..n-1} PHI(k,n)^2 where PHI(k,n) = phi(n)*mu(n/GCD(k,n))/phi(n/GCD(k,n)), and has been considered by C. Nicol under the name G(n). - _Michel Marcus_, Nov 11 2012
%F From _Amiram Eldar_, Dec 21 2023: (Start)
%F a(n) = A002618(n) - A127473(n).
%F Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = A059956 - A065464 = 0.179677... . (End)
%e a(8) = phi(8)*(8 - phi(8)) = 4*4 = 16.
%t a[n_] := Module[{phi = EulerPhi[n]}, phi*(n - phi)]; Array[a, 100] (* _Amiram Eldar_, Dec 21 2023 *)
%o (PARI) a(n) = eulerphi(n)*(n-eulerphi(n));
%Y Cf. A000010, A002618, A051953, A127473.
%Y Cf. A059956, A065464.
%K nonn,easy
%O 1,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 23 2006
%E Offset corrected by _Georg Fischer_, Mar 17 2023
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