A057000 a(n) = phi(n+1) - phi(n).

0, 1, 0, 2, -2, 4, -2, 2, -2, 6, -6, 8, -6, 2, 0, 8, -10, 12, -10, 4, -2, 12, -14, 12, -8, 6, -6, 16, -20, 22, -14, 4, -4, 8, -12, 24, -18, 6, -8, 24, -28, 30, -22, 4, -2, 24, -30, 26, -22, 12, -8, 28, -34, 22, -16, 12, -8, 30, -42, 44, -30, 6, -4, 16, -28, 46, -34, 12, -20, 46, -46, 48, -36, 4

Offset: 1

Author

N. J. A. Sloane, Sep 09 2000

Keywords

• sign

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Crossrefs

Cf. A000010, A001274.

Programs

Magma

[(EulerPhi(n+1) - EulerPhi(n)): n in [1..100]]; // Vincenzo Librandi, Sep 30 2013

Maple

A057000 := proc(n)
    numtheory[phi](n+1)-numtheory[phi](n) ;
end proc:
seq(A057000(n),n=1..40) ; # R. J. Mathar, May 10 2023

Mathematica

Table[EulerPhi[n + 1] - EulerPhi[n], {n, 100}] (* Vincenzo Librandi, Sep 30 2013 *)

PARI

a(n) = eulerphi(n+1) - eulerphi(n); \\ Michel Marcus, Jan 29 2017

Formula

G.f.: -1 + (1 - x)*Sum_{k>=1} mu(k)*x^(k-1)/(1 - x^k)^2. - Ilya Gutkovskiy, Jan 29 2017