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%I #26 Apr 08 2024 09:13:45
%S 5,7,9,11,13,17,19,21,22,23,25,26,27,29,31,34,35,37,38,39,41,43,44,45,
%T 46,47,49,50,52,53,55,57,58,59,61,62,63,65,67,68,69,71,73,74,76,77,79,
%U 81,82,83,85,86,87,88,89,91,92,93,94,95,97,98,99,100,101,103,104,106
%N Numbers whose cototient of totient is strictly greater than totient of cototient.
%C All prime numbers greater than 3 are in this sequence. Given p prime, it is easy to see that phi(p) = p - 1 and therefore the cototient of p is 1. For p > 3, phi(p) = 2q, with q > 1 an odd number not necessarily prime. Then 2q - 1 > 2q - phi(2q) > 1. - _Alonso del Arte_, Jun 02 2013
%H Harry J. Smith, <a href="/A065155/b065155.txt">Table of n, a(n) for n = 1..1000</a>
%F Numbers k such that phi(k) - phi(phi(k)) > phi(k - phi(k)) or A051953(A000010(k)) > A000010(A051953(k)).
%e 11 is in the sequence, since phi(11) = 10, cototient(11) = 1, phi(1) = 1 < cototient(10) = 4.
%t eu[n_] := EulerPhi[n]; co[n_] := n - EulerPhi[n]; A065152 = Table[co[eu[w]] - eu[co[w]], {w, 1, 256}]; Flatten[Position[Sign[A065152], 1]]
%t (* alternative program *)
%t Select[Range[100], EulerPhi[#] - EulerPhi[EulerPhi[#]] > EulerPhi[# - EulerPhi[#]] &] (* _Alonso del Arte_, Jun 02 2013 *)
%o (PARI) { n=0; for (m = 2, 10^9, t=eulerphi(m); c=m - t; if (t - eulerphi(t) > eulerphi(c), write("b065155.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 13 2009
%Y Cf. A000010, A051953, A065152, A065153, A065154.
%K nonn
%O 1,1
%A _Labos Elemer_, Oct 19 2001
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