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%I #35 Jan 15 2019 01:01:02
%S 1,1,2,2,2,4,4,4,4,6,6,6,6,8,8,8,8,8,10,10,12,12,12,12,12,12,16,16,16,
%T 16,16,16,18,18,18,18,20,20,20,20,20,22,22,24,24,24,24,24,24,24,24,24,
%U 24,28,28,30,30,32,32,32,32,32,32,32,36,36,36,36,36,36,36,36
%N All values attained by the phi(n) function, in ascending order.
%C Write down phi(1), phi(2), phi(3), ..., then sort this list. Of course the list before sorting is simply sequence A000010.
%C To ensure that all terms are found, the values of phi(n) should be computed for all n up to a primorial p# -- which are the local minima of the phi function. Selecting and sorting the values of phi(n) <= phi(p#) produces the terms of this sequence. - _T. D. Noe_, Mar 22 2011
%C A002202(n) occurs A058277(n) times. - _Reinhard Zumkeller_, Nov 22 2015
%H Zak Seidov, <a href="/A007614/b007614.txt">Table of n, a(n) for n=1..9999</a> (values up to 5152)
%t Cases[Sort[Table[EulerPhi[n],{n,1,36^2}]], n_ /; n<=36 ] (* _Jean-François Alcover_, Mar 22 2011 *)
%t A007614[m_]:=Select[Sort[Table[EulerPhi[n],{n,Prime[m]}]],#≤m&]; A007614[1000] (* _Zak Seidov_, Mar 22 2011 *)
%t primorial = Times @@ Prime[Range[4]]; phi = EulerPhi[primorial]; Sort[Select[EulerPhi[Range[primorial]], # <= phi &]] (* _T. D. Noe_, Mar 22 2011 *)
%o (PARI) (See A032447).
%o (Haskell)
%o import Data.List.Ordered (insertBag)
%o a007614 n = a007614_list !! (n-1)
%o a007614_list = f [1..] a002110_list [] where
%o f xs'@(x:xs) ps'@(p:ps) us
%o | x < p = f xs ps' $ insertBag (a000010' x) us
%o | otherwise = vs ++ f xs' ps ws
%o where (vs, ws) = span (<= a000010' x) us
%o -- _Reinhard Zumkeller_, Nov 22 2015
%Y Corresponding values of n are given by A032447. Cf. A000010.
%Y Cf. A002110, A002202, A058277 (run lengths).
%K nonn,easy,nice
%O 1,3
%A _Walter Nissen_
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