A053196 Cototients of even numbers.

1, 2, 4, 4, 6, 8, 8, 8, 12, 12, 12, 16, 14, 16, 22, 16, 18, 24, 20, 24, 30, 24, 24, 32, 30, 28, 36, 32, 30, 44, 32, 32, 46, 36, 46, 48, 38, 40, 54, 48, 42, 60, 44, 48, 66, 48, 48, 64, 56, 60, 70, 56, 54, 72, 70, 64, 78, 60, 60, 88, 62, 64, 90, 64, 82, 92, 68, 72, 94, 92, 72, 96

Offset: 1

Author

Labos Elemer, Mar 02 2000

Keywords

• nonn
• easy

Comments

Not all even numbers arise as cototient values: see A005278.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A051953, A005278.

Programs

Magma

[2*n-EulerPhi(2*n): n in [1..80]]; // Vincenzo Librandi, Jul 28 2013

Mathematica

Table[(2 n - EulerPhi[2 n]), {n, 1, 80}] (* Vincenzo Librandi, Jul 27 2013 *)

PARI

a(n) = 2*n - eulerphi(2*n) \\ Michel Marcus, Jul 26 2013

Formula

a(n) = 2n - phi(2n) = A051953(2n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 2 - 8/Pi^2 = 1.1894305... . - Amiram Eldar, Dec 21 2023