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

1,4

Links

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

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

Example

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.

Mathematica

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

Prog

(PARI) A053193(n) = { 2*n+1 - eulerphi(2*n+1)} \\ Michel Marcus, Jul 26 2013
(Magma) [2*n+1-EulerPhi(2*n+1): n in [1..90]]; // Vincenzo Librandi, Aug 16 2017

Crossrefs

Cf. A051953, A217739.

Sequence in context: A255918 A102479 A228902 * A348649 A010273 A046143

Adjacent sequences: A053190 A053191 A053192 * A053194 A053195 A053196

Keyword

nonn,easy

Author

Labos Elemer, Mar 02 2000

Status

approved