A378510 - OEIS

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

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OFFSET

2,1

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.

FORMULA

a(n) >= A007374(n).

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A304836 A010018 A256649 * A232778 A232775 A383677

Adjacent sequences: A378507 A378508 A378509 * A378511 A378512 A378513

KEYWORD

nonn

AUTHOR

Amiram Eldar, Nov 29 2024

STATUS

approved