A328858 Numbers with a record number of distinct values of the Euler totient function applied to their divisors (A319696).

1, 3, 8, 15, 32, 45, 72, 105, 144, 216, 288, 432, 792, 864, 1296, 1584, 1728, 2376, 2592, 3168, 4752, 9504, 14256, 19008, 28512, 38016, 54000, 57024, 85536, 108000, 114048, 162000, 171072, 216000, 218592, 228096, 324000, 342144, 437184, 465696, 648000, 655776

Offset: 1

Author

Amiram Eldar, Oct 28 2019

Keywords

• nonn

Comments

The corresponding record values are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 21, 22, 26, 32, 34, 38, 42, 44, 45, 50, 52, 54, 58, 59, 62, 63, 64, 66, 71, 72, 76, 78, 83, 84, ...

Examples

			The first 10 terms of A319696(k) are 1, 1, 2, 2, 2, 2, 2, 3, 3, 2. The record values 1, 2, and 3 are obtained at k = 1, 3, and 8. Therefore this sequence begins with 1, 3, 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000010, A102190, A319696.

Programs

Mathematica

f[n_] := Length @ Union[EulerPhi /@ Divisors[n]]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 660000}]; s