cp's OEIS Frontend

A317013 For successive terms of A002202, totient values t, lcm({x: phi(x)=t})/gcd({x: phi(x)=t}).

%I A317013 #9 Jul 23 2018 02:49:55
%S A317013 2,12,120,126,240,2,3276,8160,1026,3300,2,32760,2,2,16320,531468,
%T A317013 270600,4214,12,2,65520,2,2,12,2,5241852,32640,2,2,5043631320,2,
%U A317013 541200,2,25284,245640,12,216084960,25250,2,12,2,4697028,2,393240,12,3407203800,2,65280,2,388332
%N A317013 For successive terms of A002202, totient values t, lcm({x: phi(x)=t})/gcd({x: phi(x)=t}).
%C A317013 From _Torlach Rush_, Jul 03 2018: (Start)
%C A317013 Consider the quotients q(t) = lcm({x: phi(x)=t})/gcd({x: phi(x)=t}).
%C A317013 When the number of solutions is 2, q(t) must be 2. For example invphi(10) = [11, 22], and q(10)=2.
%C A317013 When the number of solutions is 3, the solutions are x1 < x2 < (2 * x1) and the only observed value of q(t) is 12. For example, invphi(44) = [69, 92, 138], and q(44)=12.
%C A317013 When the number of solutions is greater than 3, multiple values of q(t) are observed. (End)
%H A317013 Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts for various problems</a>
%e A317013 invphi(1) = [1, 2] and lcm(1, 2) / gcd(1, 2) is 2.
%t A317013 Map[LCM[##]/GCD[##] & @@ # &, Take[Values@ KeySort@ PositionIndex@ Array[EulerPhi, 10^6], 50]] (* _Michael De Vlieger_, Jul 20 2018 *)
%o A317013 (PARI) lista(nn) = {for (n=1, nn, my(v = invphi(n)); if (#v, print1(lcm(v)/gcd(v), ", ")););}
%Y A317013 Cf. A000010, A002202, A032447.
%K A317013 nonn
%O A317013 1,1
%A A317013 _Michel Marcus_, Jul 19 2018