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A065153 Numbers for which the cototient of the totient is equal to the  totient of the cototient. 4
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 (list; graph; refs; listen; history; text; internal format)
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]] (* Labos *)

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

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Last modified May 16 19:38 EDT 2021. Contains 343951 sequences. (Running on oeis4.)