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%I #38 Dec 15 2023 06:19:07
%S 0,2,3,8,5,24,7,32,27,60,11,96,13,112,105,128,17,216,19,240,189,264,
%T 23,384,125,364,243,448,29,660,31,512,429,612,385,864,37,760,585,960,
%U 41,1260,43,1056,945,1104,47,1536,343,1500,969,1456,53,1944,825,1792,1197
%N Cototient function of n^2.
%C Seems to be invertible like n*Phi(n). Compare with A002618, A038040.
%H Reinhard Zumkeller, <a href="/A053650/b053650.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n*(n - phi(n)) = n^2 - n*phi(n) = Cototient(n^2) = A051953(A000290(n)).
%F a(n) = n^2 - A002618(n).
%F For p prime, Cototient(p)=1 and a(p)=p.
%F a(n) = n*cototient(n) = n*A051953(n). - _Omar E. Pol_, Nov 22 2012
%F Dirichlet g.f.: zeta(s-2)*(1 - 1/zeta(s-1)). - _Ilya Gutkovskiy_, Jul 26 2016
%F Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = 1 - 6/Pi^2 (A229099). - _Amiram Eldar_, Dec 15 2023
%t Table[n(n-EulerPhi[n]), {n, 60}] (* _Michael De Vlieger_, Jul 26 2016 *)
%o (PARI) a(n) = n^2 - eulerphi(n^2) \\ _Michel Marcus_, Jul 27 2013
%o (Haskell)
%o a053650 = a051953 . a000290 -- _Reinhard Zumkeller_, Jan 21 2014
%o (Magma) [n*(n-EulerPhi(n)): n in [1..60]]; // _Vincenzo Librandi_, Jul 27 2016
%o (Sage) [n*(n - euler_phi(n)) for n in (1..60)] # _G. C. Greubel_, May 18 2019
%o (GAP) List([1..60], n-> n*(n- Phi(n)) ); # _G. C. Greubel_, May 18 2019
%Y Cf. A000005, A038040.
%Y Cf. A001248, A002618, A053650, A053192, A053193, A036689, A229099.
%K nonn,look,easy
%O 1,2
%A _Labos Elemer_, Feb 18 2000
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