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%I #8 Sep 25 2021 04:45:34
%S 1,3,8,15,32,45,72,105,144,216,288,432,792,864,1296,1584,1728,2376,
%T 2592,3168,4752,9504,14256,19008,28512,38016,54000,57024,85536,108000,
%U 114048,162000,171072,216000,218592,228096,324000,342144,437184,465696,648000,655776
%N Numbers with a record number of distinct values of the Euler totient function applied to their divisors (A319696).
%C 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, ...
%H Amiram Eldar, <a href="/A328858/b328858.txt">Table of n, a(n) for n = 1..100</a>
%e 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.
%t 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
%Y Cf. A000010, A102190, A319696.
%K nonn
%O 1,2
%A _Amiram Eldar_, Oct 28 2019
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