A110175 Composite numbers n such that the equation phi(n)=phi(k)+phi(n-k) has no solution, where phi is Euler's totient function.

6, 30, 49, 81, 91, 95, 115, 121, 155, 187, 205, 210, 221, 243, 254, 259, 287, 298, 299, 329, 341, 355, 361, 377, 403, 415, 437, 451, 469, 473, 502, 533, 551, 559, 565, 611, 625, 629, 649, 655, 662, 667, 674, 679, 685, 703, 713, 731, 737, 746, 767, 779, 781

Offset: 1

Author

T. D. Noe, Jul 15 2005

Keywords

• nonn

Comments

The only prime for which this equation has a solution is 3.

Crossrefs

Cf. A110173 (least k such that phi(n)=phi(k)+phi(n-k)).

Programs

Mathematica

a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; t=Table[Length[a[n]], {n, 1000}]; Complement[Flatten[Position[t, 0]], Prime[Range[PrimePi[1000]]]]