A362489 - OEIS

%I #11 Apr 22 2023 11:39:03

%S 5,1,6,12,36,24,396,48,216,96,528,144,384,2784,432,240,1296,288,1584,

%T 1800,480,1680,1080,864,576,3240,2016,960,6624,720,1152,7776,12000,

%U 8448,5280,1728,10752,2304,4032,4800,6048,3840,2160,5184,4608,6336,1440,10560,29568

%N 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.

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

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

%H Amiram Eldar, <a href="/A362489/b362489.txt">Table of n, a(n) for n = 0..300</a>

%t 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 *)

%Y Cf. A091732, A362484, A362485.

%Y Similar sequences: A007374, A063507, A361970, A362186.

%K nonn

%O 0,1

%A _Amiram Eldar_, Apr 22 2023