A362489 a(n) is the least number k such that the equation iphi(x) = k has exactly 2*n solutions, or -1 if no such k exists, where iphi is the infinitary totient function A091732.

5, 1, 6, 12, 36, 24, 396, 48, 216, 96, 528, 144, 384, 2784, 432, 240, 1296, 288, 1584, 1800, 480, 1680, 1080, 864, 576, 3240, 2016, 960, 6624, 720, 1152, 7776, 12000, 8448, 5280, 1728, 10752, 2304, 4032, 4800, 6048, 3840, 2160, 5184, 4608, 6336, 1440, 10560, 29568

Offset: 0

Author

Amiram Eldar, Apr 22 2023

Keywords

• nonn

Comments

a(n) is the least number k such that A362485(k) = 2*n. Odd values of A362485 are impossible.

Is there any n for which a(n) = -1?

Links

• Amiram Eldar, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A091732, A362484, A362485.

Similar sequences: A007374, A063507, A361970, A362186.

Programs

Mathematica

solnum[n_] := Length[invIPhi[n]]; seq[len_, kmax_] := Module[{s = Table[-1, {len}], c = 0, k = 1, ind}, While[k < kmax && c < len, ind = solnum[k]/2 + 1; If[ind <= len && s[[ind]] < 0, c++; s[[ind]] = k]; k++]; s]; seq[50, 10^5] (* using the function invIPhi from A362484 *)