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

30, 116, 42, 456, 780, 1140, 1368, 1380, 3420, 4356, 5104, 20196, 9396, 1980, 15876, 8316, 4860, 16380, 79464, 239976, 15720, 69300, 129960, 70000, 90360, 141680, 263160, 835380, 802296, 706680, 236808, 39960, 205800, 2898840, 3200904, 598920, 664440, 2723400

Offset: 2

Author

Amiram Eldar, Nov 29 2024

Keywords

• nonn

Comments

The least term k of A378509 such that A014197(k) = n.

Links

• Amiram Eldar, Table of n, a(n) for n = 2..70
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).
• David M. Bressoud, A Course in Computational Number Theory (web page), CNT.m, Computational Number Theory Mathematica package.

Crossrefs

Cf. A000010, A002202, A007374, A007617, A014197, A378509.

Programs

Mathematica

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 *)

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

Formula

a(n) >= A007374(n).