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A210719 Numbers n for which phi(n) is different from phi(m) for all m < n.

%I A210719 #26 Dec 18 2012 02:38:51
%S A210719 1,3,5,7,11,13,15,17,19,23,25,29,31,35,37,41,43,47,51,53,59,61,65,67,
%T A210719 69,71,73,79,81,83,85,87,89,97,101,103,107,109,113,121,123,127,129,
%U A210719 131,137,139,141,143,149,151,157,159,161,163,167,173,177,179,181,185
%N A210719 Numbers n for which phi(n) is different from phi(m) for all m < n.
%C A210719 In the definition, phi(n) is Euler's totient function (A000010).
%C A210719 Also, the positions where phi(n) attains a new value.
%C A210719 All terms are odd.
%C A210719 The sequence of odd primes (A065091) is a subsequence.
%H A210719 T. D. Noe, <a href="/A210719/b210719.txt">Table of n, a(n) for n = 1..1000</a>
%F A210719 A090127(n) = A000010(a(n)).
%e A210719 7 is in the sequence because phi(7) = 6, and 7 is the smallest n such that phi(n) = 6 (the sequence A000010 starts 1, 1, 2, 2, 4, 2, 6, ...).
%t A210719 nn = 185; s = EulerPhi[Range[nn]]; Select[Range[nn], ! MemberQ[Take[s, # - 1], s[[#]]] &] (* _T. D. Noe_, Dec 17 2012 *)
%o A210719 (Scheme with _Antti Karttunen_'s intseq-library): (define A210719 (DISTINCT-POS 1 1 A000010))
%o A210719 (PARI) is_a210719(n) = {local(i,r,p);r=1;p=eulerphi(n);for(i=1,n-1,if(eulerphi(i)==p,r=0));r} \\ _Michael B. Porter_, Dec 16 2012
%o A210719 (Haskell)
%o A210719 a210719 n = a210719_list !! (n-1)
%o A210719 a210719_list = f (zip [1..] a000010_list) [] where
%o A210719    f ((i,x):ixs) phis | x `elem` phis = f ixs phis
%o A210719                       | otherwise     = i : f ixs (x : phis)
%o A210719 -- _Reinhard Zumkeller_, Dec 18 2012
%Y A210719 Cf. A000010, A090127.
%K A210719 nonn
%O A210719 1,2
%A A210719 _Antti Karttunen_, Dec 16 2012