A048867 Numbers for which reduced residue system contains fewer primes than nonprimes.

1, 2, 11, 13, 17, 19, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 94, 95, 97, 99, 101, 103, 106, 107, 109, 111, 113, 115, 117, 118, 119, 121, 122, 123, 124, 125, 127, 128

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

Integers n such that 2*A000720(n) - 2*A001221(n) < A000010(n).

Examples

			Large primes belong to this set. Composites like: n=35 has 2 prime divisors, Phi(35)=24 Pi(35)=11; In reduced residue system 9 primes and 15 nonprimes occur.
		

Links

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

Crossrefs

Cf. A000010, A000720, A001221.

Programs

Mathematica

Select[Range[500], 2*PrimePi[#] - 2*PrimeNu[#] < EulerPhi[#] &] (* G. C. Greubel, May 12 2017 *)

PARI

isok(n) = 2*(primepi(n) - omega(n)) < eulerphi(n); \\ Michel Marcus, May 13 2017