%I #21 Apr 20 2023 04:23:32
%S 2,110,506,2162,3422,4970,6806,11342,13310,17030,27722,31862,36290,
%T 51302,56882,62750,68906,96410,120062,128522,146306,175142,185330,
%U 195806,217622,228962,240590,252506,267674,316406,343982,358202,417962,433622,465806,516242
%N Numbers of the form 12*k + 2 with nonempty inverse totient set.
%C Except for the first term, each of these sets contains 2 terms. Other numbers of the form 12*k + 2 have empty inverse totient sets.
%C From _Jianing Song_, Dec 30 2018: (Start)
%C Except for the first term, these are numbers of the form (p - 1)*p^(2*e-1) = phi(p^(2*e)) where p is a prime congruent to 11 modulo 12. The inverse totient set for a(n) (n > 1) is {p^(2*e), 2*p^(2*e)}.
%C Numbers k such that A063667((k-2)/12) != 0.
%C The number of terms <= N is roughly (1/8)*sqrt(N)/log(N). (End)
%H Jianing Song, <a href="/A063668/b063668.txt">Table of n, a(n) for n = 1..315</a> (All terms below 10^8.)
%e 1407782 = 1186*1187 where 1187 is a prime congruent to 11 modulo 12, so 1407782 is a term, with invphi(1407782) = {1408969, 2817938} = {1187^2, 2*1187^2}.
%e 267674 = 22*23^3 where 23 is a prime congruent to 11 modulo 12, so 267674 is a term, with invphi(267674) = {279841, 559682} = {23^4, 2*23^4}. - _Jianing Song_, Dec 30 2018
%o (PARI) A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1)
%o isok(n) = my(p=A006530(n), e=if(n>1, valuation(n,p), 1)); (n==2) || (p%12==11&&e%2&&n==(p-1)*p^e) \\ _Jianing Song_, Dec 30 2018
%o (PARI) isok(n) = #invphi(n) && !((n-2) % 12); \\ _Michel Marcus_, Dec 30 2018; using the invphi script by Max Alekseyev
%o (PARI) isok(m) = !((m-2) % 12) && istotient(m); \\ _Michel Marcus_, Apr 20 2023
%Y Cf. A000010, A063667.
%K nonn
%O 1,1
%A _Labos Elemer_, Aug 22 2001
%E Three missing terms added by _Jianing Song_, Dec 30 2018