A053192 - OEIS

%I #24 Dec 15 2023 06:18:59

%S 0,4,9,32,25,144,49,256,243,600,121,1152,169,1568,1575,2048,289,3888,

%T 361,4800,3969,5808,529,9216,3125,9464,6561,12544,841,19800,961,16384,

%U 14157,20808,13475,31104,1369,28880,22815,38400,1681,52920,1849,46464

%N a(n) is the cototient of n^3.

%C For n^k, n^k - EulerPhi(n^k) = n^(k-1)*(n-EulerPhi(n)), or cototient(n^k) = n^(k-1)*cototient(n). A similar relation holds for Euler totient function.

%H Vincenzo Librandi, <a href="/A053192/b053192.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n^2*Cototient(n) = A051953(n^3) = n^3 - EulerPhi(n^3) = Cototient(n^3).

%F a(prime(n)) = A051953(prime(n)^3) = A001248(n).

%F Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = 1 - 6/Pi^2 (A229099). - _Amiram Eldar_, Dec 15 2023

%t Table[(n^3 - EulerPhi[n^3]), {n, 1, 50}] (* _Vincenzo Librandi_, Jul 27 2013 *)

%o (PARI) a(n) = n^3 - eulerphi(n^3) \\ _Michel Marcus_, Jul 26 2013

%o (Magma) [n^3-EulerPhi(n^3): n in [1..44]]; // _Vincenzo Librandi_, Jul 28 2013

%Y Cf. A000010, A051953, A002618, A053650, A053191, A001248, A229099.

%K nonn,easy

%O 1,2

%A _Labos Elemer_, Mar 02 2000