cp's OEIS Frontend

A007614 All values attained by the phi(n) function, in ascending order.

%I A007614 #40 Nov 15 2024 05:24:30
%S A007614 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 A007614 16,16,16,18,18,18,18,20,20,20,20,20,22,22,24,24,24,24,24,24,24,24,24,
%U A007614 24,28,28,30,30,32,32,32,32,32,32,32,36,36,36,36,36,36,36,36
%N A007614 All values attained by the phi(n) function, in ascending order.
%C A007614 Write down phi(1), phi(2), phi(3), ..., then sort this list. Of course the list before sorting is simply sequence A000010.
%C A007614 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 A007614 A002202(n) occurs A058277(n) times. - _Reinhard Zumkeller_, Nov 22 2015
%H A007614 Zak Seidov, <a href="/A007614/b007614.txt">Table of n, a(n) for n=1..9999</a> (values up to 5152)
%H A007614 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%t A007614 Cases[Sort[Table[EulerPhi[n],{n,1,36^2}]], n_ /; n<=36 ]  (* _Jean-François Alcover_, Mar 22 2011 *)
%t A007614 A007614[m_]:=Select[Sort[Table[EulerPhi[n],{n,Prime[m]}]],#≤m&]; A007614[1000] (* _Zak Seidov_, Mar 22 2011 *)
%t A007614 primorial = Times @@ Prime[Range[4]]; phi = EulerPhi[primorial]; Sort[Select[EulerPhi[Range[primorial]], # <= phi &]] (* _T. D. Noe_, Mar 22 2011 *)
%o A007614 (PARI)  (See A032447).
%o A007614 (PARI) lista(nmax) = {my(m); for(n = 1, nmax, m = invphiNum(n); for(i = 1, m, print1(n, ", ")));} \\ _Amiram Eldar_, Nov 15 2024 using _Max Alekseyev_'s invphi.gp
%o A007614 (Haskell)
%o A007614 import Data.List.Ordered (insertBag)
%o A007614 a007614 n = a007614_list !! (n-1)
%o A007614 a007614_list = f [1..] a002110_list [] where
%o A007614    f xs'@(x:xs) ps'@(p:ps) us
%o A007614      | x < p = f xs ps' $ insertBag (a000010' x) us
%o A007614      | otherwise = vs ++ f xs' ps ws
%o A007614      where (vs, ws) = span (<= a000010' x) us
%o A007614 -- _Reinhard Zumkeller_, Nov 22 2015
%Y A007614 Corresponding values of n are given by A032447.
%Y A007614 Cf. A000010. A002110, A002202, A058277 (run lengths).
%K A007614 nonn,easy,nice
%O A007614 1,3
%A A007614 _Walter Nissen_