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A194507 a(n) = y is the unique solution to y*phi(y) = A082473(n).

%I A194507 #23 Sep 29 2019 20:22:45
%S A194507 1,2,3,4,6,5,8,10,7,12,9,14,18,11,15,16,13,20,24,22,30,21,17,26,28,19,
%T A194507 36,27,25,42,23,32,34,40,33,38,48,29,35,44,31,39,60,54,50,46,45,52,66,
%U A194507 37,56,58,51,41,70,72,43,62,78,84,64,57,49,90,47,68,55,63,80
%N A194507 a(n) = y is the unique solution to y*phi(y) = A082473(n).
%C A194507 The permutation which rearranges the terms of A002618 into ascending order. - _Antti Karttunen_, Sep 28 2019
%H A194507 Antti Karttunen, <a href="/A194507/b194507.txt">Table of n, a(n) for n = 1..20001</a>
%H A194507 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A194507 From _Antti Karttunen_, Sep 28 2019: (Start)
%F A194507 a(n) = A327172(A082473(n)).
%F A194507 A002618(a(n)) = A082473(n).
%F A194507 (End)
%e A194507 a(6) = 5 because 5*phi(5) = 20 = A082473(6).
%t A194507 Block[{nn = 3000, s, t}, s = Array[EulerPhi[#] (Sqrt@ # /. (c_: 1) a_^(b_: 0) :> (c a^b)^2) &, nn]; t = TakeWhile[Union@ s, # <= nn &]; Map[Block[{y = 1}, While[y EulerPhi@ y != #, y++]; y] &, t]] (* _Michael De Vlieger_, Sep 29 2019, after _Bill Gosper_ at A007913 *)
%o A194507 (PARI)
%o A194507 up_to = 105;
%o A194507 A327172(n) = { fordiv(n,d,if(eulerphi(d)*d == n, return(d))); (0); };
%o A194507 A194507list(up_to) = { my(v=vector(up_to),k=1); for(n=1,oo,if((v[k]=A327172(n))>0,k++); if(k>up_to, return(v))); };
%o A194507 v194507 = A194507list(up_to);
%o A194507 A194507(n) = v194507[n]; \\ _Antti Karttunen_, Sep 28 2019
%Y A194507 Cf. A002618, A082473, A327173 (inverse permutation).
%Y A194507 Nonzero terms in A327172, in the order of appearance.
%K A194507 nonn
%O A194507 1,2
%A A194507 _Franz Vrabec_, Aug 27 2011