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

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

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]]]]

Crossrefs

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

Sequence in context: A070195 A241190 A276933 * A249676 A259752 A014203

Adjacent sequences: A110172 A110173 A110174 * A110176 A110177 A110178

Keyword

nonn

Author

T. D. Noe, Jul 15 2005

Status

approved