A065153 Numbers for which the cototient of the totient is equal to the totient of the cototient.

1, 3, 4, 8, 10, 14, 16, 18, 20, 28, 32, 33, 36, 40, 42, 54, 56, 64, 72, 75, 80, 84, 108, 110, 112, 114, 126, 128, 144, 160, 162, 168, 177, 198, 216, 220, 224, 228, 252, 256, 288, 320, 321, 324, 336, 342, 350, 375, 378, 396, 414, 432, 440, 448, 456, 486, 504, 512

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Formula

Numbers n such that phi(n) - phi(phi(n)) = phi(n - phi(n)) or A000010(A051953(m)) = A051953(A000010(m)).

Example

Because phi(108) = 36, 108 - phi(108) = 72 = cototient(108), cototient(36) = 36 - 12 = 24, totient(72) = 24, so 108 is the sequence.

Mathematica

eu[n_] := EulerPhi[n]; co[n_] := n - EulerPhi[n]; Flatten[Position[Table[co[eu[m]] - eu[co[m]], {m, 1, 1000}], 0]]
(* alternative program *)
Select[Range[500], EulerPhi[#] - EulerPhi[EulerPhi[#]] == EulerPhi[# - EulerPhi[#]] &] (* Alonso del Arte, Jun 12 2013 *)

Prog

(PARI) { n=0; for (m = 1, 10^9, t=eulerphi(m); c=m - t; if (m>1, f=t - eulerphi(t) - eulerphi(c), f=0); if (f==0, write("b065153.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 13 2009

Crossrefs

Cf. A000010, A051953.

Sequence in context: A114913 A111174 A075751 * A030497 A080085 A182276

Adjacent sequences: A065150 A065151 A065152 * A065154 A065155 A065156

Keyword

nonn

Author

Labos Elemer, Oct 19 2001

Status

approved