A074057 a(n) = 2*phi(n-2)-(n-1).

0, -1, 0, -1, 2, -3, 4, -1, 2, -3, 8, -5, 10, -3, 0, -1, 14, -7, 16, -5, 2, -3, 20, -9, 14, -3, 8, -5, 26, -15, 28, -1, 6, -3, 12, -13, 34, -3, 8, -9, 38, -19, 40, -5, 2, -3, 44, -17, 34, -11, 12, -5, 50, -19, 24, -9, 14, -3, 56, -29, 58, -3, 8, -1, 30, -27, 64, -5, 18, -23, 68, -25, 70, -3, 4, -5, 42, -31, 76, -17, 26, -3, 80

Offset: 3

Author

Benoit Cloitre, Sep 15 2002

Keywords

• easy
• sign

Comments

Conjecture : a(n)=0 if and only if n is a Fermat prime (A019434).

The conjecture appears to be false, a(83623937)=0 and 83623937 is not a Fermat number (A000215). See A232720 for sequence of n such that a(n)=0. - Michel Marcus, Nov 28 2013

Crossrefs

Cf. A000010.

Programs

Mathematica

Table[2*EulerPhi[n-1]-n,{n,2,90}] (* Harvey P. Dale, May 22 2020 *)

PARI

a(n) = 2*eulerphi(n-2) - (n-1); \\ Michel Marcus, Nov 28 2013

Formula

a(n)=-1 if n is of the form 2^x+2;

a(n)=-3 if n is in a subsequence b(k) = 8, 12, 16, 24, 28, 36, 40, 48, 60, 64, 76, 84, 88, 96..( b(k) seems to be asymptotic to c*n*log(n) with c=2.28..).