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A053193 Cototient of odd numbers.

%I A053193 #25 Dec 15 2023 06:19:03
%S A053193 1,1,1,3,1,1,7,1,1,9,1,5,9,1,1,13,11,1,15,1,1,21,1,7,19,1,15,21,1,1,
%T A053193 27,17,1,25,1,1,35,17,1,27,1,21,31,1,19,33,23,1,39,1,1,57,1,1,39,1,27,
%U A053193 45,23,11,43,25,1,45,1,25,63,1,1,49,23,33,63,1,1,57,35,1,55,29,1,85,1,13
%N A053193 Cototient of odd numbers.
%H A053193 Michael De Vlieger, <a href="/A053193/b053193.txt">Table of n, a(n) for n = 1..10000</a>
%F A053193 a(n) = cototient(2n+1) = A051953(2n+1).
%F A053193 Sum_{k=1..n} a(k) ~ c * n^2, where c = 1 - 8/Pi^2. - _Amiram Eldar_, Dec 15 2023
%e A053193 n=12, 2n+1=25, phi(25)=20, cototient(25)=25-20=5,  a(12)=5.
%e A053193 n=16, 2n+1=33, phi(33)=20, cototient(33)=33-20=13, a(16)=13.
%t A053193 Table[# - EulerPhi@ # &[2 n + 1], {n, 84}] (* _Michael De Vlieger_, Aug 15 2017 *)
%o A053193 (PARI) A053193(n) = { 2*n+1 - eulerphi(2*n+1)} \\ _Michel Marcus_, Jul 26 2013
%o A053193 (Magma) [2*n+1-EulerPhi(2*n+1): n in [1..90]]; // _Vincenzo Librandi_, Aug 16 2017
%Y A053193 Cf. A051953, A217739.
%K A053193 nonn,easy
%O A053193 1,4
%A A053193 _Labos Elemer_, Mar 02 2000