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A378510 The least totient number k with exactly n solutions to the equation phi(x) = k, where all the solutions are nontotient numbers (A007617).

%I A378510 #11 Nov 30 2024 06:26:35
%S A378510 30,116,42,456,780,1140,1368,1380,3420,4356,5104,20196,9396,1980,
%T A378510 15876,8316,4860,16380,79464,239976,15720,69300,129960,70000,90360,
%U A378510 141680,263160,835380,802296,706680,236808,39960,205800,2898840,3200904,598920,664440,2723400
%N A378510 The least totient number k with exactly n solutions to the equation phi(x) = k, where all the solutions are nontotient numbers (A007617).
%C A378510 The least term k of A378509 such that A014197(k) = n.
%H A378510 Amiram Eldar, <a href="/A378510/b378510.txt">Table of n, a(n) for n = 2..70</a>
%H A378510 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%H A378510 David M. Bressoud, <a href="https://www.davidbressoud.org/books-videos">A Course in Computational Number Theory (web page)</a>, <a href="https://drive.google.com/file/d/1UMesJ93mpdCabQvETMqOBH8eCR4JWA6X/view?usp=sharing">CNT.m</a>, Computational Number Theory Mathematica package.
%F A378510 a(n) >= A007374(n).
%t A378510 seq[len_] := Module[{v = Table[0, {len+1}], c = 0, k = 2, s, ns}, While[c < len, s = PhiInverse[k]; ns = Length[s]; If[0 < ns <= len + 1 && AllTrue[s, PhiMultiplicity[#] == 0 &] && v[[ns]] == 0, v[[ns]] = k; c++]; k += 2]; Rest[v]]; seq[10] (* using David M. Bressoud's CNT.m *)
%o A378510 (PARI) lista(len) = {my(v = vector(len+1), c = 0, k = 2, s, ns, ans); while(c < len, s = invphi(k); ns = #s; ans = 1; for(i = 1, ns, if(istotient(s[i]), ans = 0; break)); if(ans && ns > 0 && ns <= len + 1 && v[ns] == 0, c++; v[ns] = k); k += 2); vecextract(v,"^1");} \\ using _Max Alekseyev_'s invphi.gp
%Y A378510 Cf. A000010, A002202, A007374, A007617, A014197, A378509.
%K A378510 nonn
%O A378510 2,1
%A A378510 _Amiram Eldar_, Nov 29 2024