A048866 Difference between number of nonprimes and primes in reduced residue system of n.

1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 2, -2, 0, -2, 4, -4, 4, -4, 0, -2, 6, -6, 4, -2, 2, -2, 10, -6, 10, -4, 2, -2, 6, -6, 14, -2, 4, -4, 16, -8, 16, -4, 0, -2, 18, -10, 14, -6, 6, -2, 22, -10, 12, -4, 8, 0, 26, -12, 26, -2, 4, -2, 16, -10, 30, -2, 10, -8, 32, -12, 32, -2, 2, -2

Offset: 1

Author

Labos Elemer

Keywords

• sign

Examples

			n = 31: Phi(31) = 30 from which 10 is prime and 20 is not: a(31) = 20-10 = 10;
n = 20: Phi(20) = 8 from which 6 are primes and 2 are not: a(20) = 2-6 = -4;
n = 15: reduced residue system = {1,2,7,4,8,11,13,14}, primes = {2,7,11,13,}, nonprimes = {2,4,8,14}, thus a(15) = 4-4 = 0.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A000720, A001221.

Programs

Mathematica

Table[EulerPhi[n] - 2*PrimePi[n] + 2*PrimeNu[n] , {n,1,50}] (* G. C. Greubel, May 12 2017 *)

Formula

a(n) = A000010(n) - 2*A000720(n) + 2* A001221(n).