A219428 a(n) = n - 1 - phi(n).

-1, 0, 0, 1, 0, 3, 0, 3, 2, 5, 0, 7, 0, 7, 6, 7, 0, 11, 0, 11, 8, 11, 0, 15, 4, 13, 8, 15, 0, 21, 0, 15, 12, 17, 10, 23, 0, 19, 14, 23, 0, 29, 0, 23, 20, 23, 0, 31, 6, 29, 18, 27, 0, 35, 14, 31, 20, 29, 0, 43, 0, 31, 26, 31, 16, 45, 0, 35, 24, 45, 0, 47

Offset: 1

Author

V. Raman, Nov 20 2012

Keywords

• sign
• easy

Comments

Apart from the first term, the same as A016035.

For n > 1, a(n) is also the number of numbers below n which are not coprime to n.

a(n) = 0 if n is prime.

x^(n - 1 - phi(n)) is congruent to x^(n - 1) mod n, if x is coprime to n, since x^phi(n) is congruent to 1 (mod n) if x is coprime to n.

Links

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

Crossrefs

Cf. A000010, A219029.

Programs

Magma

[(n - 1 - (EulerPhi(n))): n in [1..100]]; // Vincenzo Librandi, Jan 26 2013

Mathematica

Table[n - (EulerPhi[n] + 1), {n, 75}] (* Alonso del Arte, Nov 17 2012 *)

PARI

for(n=1,100,print1(n-1-eulerphi(n)","))

Formula

a(n) = n - 1 - A000010(n) = A051953(n) - 1 = cototient(n) - 1. - Omar E. Pol, Nov 21 2012