A362487 Infinitary highly totient numbers: numbers k that have more solutions x to the equation iphi(x) = k than any smaller k, where iphi is the infinitary totient function A091732.

1, 6, 12, 24, 48, 96, 144, 240, 288, 480, 576, 720, 1152, 1440, 2880, 4320, 5760, 8640, 11520, 17280, 34560, 51840, 69120, 103680, 120960, 172800, 207360, 241920, 345600, 362880, 414720, 483840, 725760, 967680, 1209600, 1451520, 1935360, 2419200, 2903040, 3628800

Offset: 1

Author

Amiram Eldar, Apr 22 2023

Keywords

• nonn

Comments

Indices of records of A362485.

The corresponding numbers of solutions are 2, 4, 6, 10, 14, 18, 22, ... (A362488).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A091732, A362484, A362485, A362486, A362488.

Similar sequences: A097942, A100827, A361968, A362183.

Programs

Mathematica

solnum[n_] := Length[invIPhi[n]]; seq[kmax_] := Module[{s = {}, solmax=0}, Do[sol = solnum[k]; If[sol > solmax, solmax = sol; AppendTo[s, k]], {k, 1, kmax}]; s]; seq[10^4] (* using the function invIPhi from A362484 *)