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

1,2

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, ...

Links

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

Example

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.

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

Crossrefs

Cf. A000010, A102190, A319696.

Sequence in context: A196087 A295735 A309052 * A277224 A090741 A255835

Adjacent sequences: A328855 A328856 A328857 * A328859 A328860 A328861

Keyword

nonn

Author

Amiram Eldar, Oct 28 2019

Status

approved