%I
%S 1,2,4,6,8,12,16,18,20,24
%N Positive integers m such that whenever n is in the range of the Euler totient function, so is m*n.
%C Closure under multiplication: if multiplication by m_1 carries totient values to totient values and multiplication by m_2 does also, then so does their composition, which is multiplication by m_1*m_2.
%C No odd terms are in the sequence except for 1.
%C 32, 36, 40, 42, 48, 54, 64, and 72 are also in this sequence, although determining their position is difficult.  _Charlie Neder_, Aug 04 2019
%e 1 is trivially in the sequence.
%e Note that any value assumed by phi is assumed at an even argument, since k odd implies phi(k) = phi(2k).
%e Then 2 is in the sequence, since n = phi(k) and k even imply that 2n = phi(2k).
%e 3 is not in the sequence: 30 = phi(31), but 90 is not in the range of phi.
%e 4 is in the sequence because 2 is (using closure under multiplication).
%e 5 is not in the sequence: 18 = phi(19), but 90 is not in the range of phi.
%e 6 is in the sequence: If n = phi(k) with k even, phi(9k) = 6n if k is a nonmultiple of 3. If k is a multiple of 3, then 6n = phi(6k) since k is a multiple of 6.
%e 7 is not in the sequence: 22 = phi(23), but 154 is not in the range of phi.
%e 8 is in the sequence because 2 is.
%K nonn,more
%O 1,2
%A _David L. Harden_, Mar 24 2018
