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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.
1
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.
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Jul 15 2005
STATUS
approved