A053193 Cototient of odd numbers.

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, 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, 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

Offset: 1

Author

Labos Elemer, Mar 02 2000

Keywords

• nonn
• easy

Examples

			n=12, 2n+1=25, phi(25)=20, cototient(25)=25-20=5,  a(12)=5.
n=16, 2n+1=33, phi(33)=20, cototient(33)=33-20=13, a(16)=13.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A051953, A217739.

Programs

Magma

[2*n+1-EulerPhi(2*n+1): n in [1..90]]; // Vincenzo Librandi, Aug 16 2017

Mathematica

Table[# - EulerPhi@ # &[2 n + 1], {n, 84}] (* Michael De Vlieger, Aug 15 2017 *)

PARI

A053193(n) = { 2*n+1 - eulerphi(2*n+1)} \\ Michel Marcus, Jul 26 2013

Formula

a(n) = cototient(2n+1) = A051953(2n+1).

Sum_{k=1..n} a(k) ~ c * n^2, where c = 1 - 8/Pi^2. - Amiram Eldar, Dec 15 2023