This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063668 #27 Dec 15 2024 07:26:25
%S A063668 2,110,506,2162,3422,4970,6806,11342,13310,17030,27722,31862,36290,
%T A063668 51302,56882,62750,68906,96410,120062,128522,146306,175142,185330,
%U A063668 195806,217622,228962,240590,252506,267674,316406,343982,358202,417962,433622,465806,516242
%N A063668 Numbers of the form 12*k + 2 with nonempty inverse totient set.
%C A063668 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 A063668 From _Jianing Song_, Dec 30 2018: (Start)
%C A063668 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 A063668 Numbers k such that A063667((k-2)/12) != 0.
%C A063668 The number of terms <= N is roughly (1/8)*sqrt(N)/log(N). (End)
%H A063668 Amiram Eldar, <a href="/A063668/b063668.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..315 from Jianing Song)
%e A063668 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 A063668 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 A063668 (PARI) A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1)
%o A063668 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 A063668 (PARI) isok(n) = #invphi(n) && !((n-2) % 12); \\ _Michel Marcus_, Dec 30 2018; using the invphi script by Max Alekseyev
%o A063668 (PARI) isok(m) = !((m-2) % 12) && istotient(m); \\ _Michel Marcus_, Apr 20 2023
%Y A063668 Cf. A000010, A063667.
%K A063668 nonn
%O A063668 1,1
%A A063668 _Labos Elemer_, Aug 22 2001
%E A063668 Three missing terms added by _Jianing Song_, Dec 30 2018