A348002 Numbers with a record number of distinct values of the unitary totient function applied to their unitary divisors (A348001).

1, 3, 12, 60, 420, 660, 4620, 8580, 9240, 60060, 78540, 106260, 157080, 1021020, 1381380, 1492260, 1806420, 2762760, 2984520, 23483460, 34321980, 38798760, 46966920, 68643960, 681020340, 892371480, 1848483780, 1990674840, 2127962760, 3226266120

Offset

1,2

Comments

The corresponding record values are 1, 2, 4, 8, 13, 16, 26, 28, 32, 40, 50, 52, 64, 72, 80, 84, 100, 104, 128, 144, 168, 176, 200, 256, 288, 352, 360, 416, 424, 512, ...

This sequence is infinite since A348001 is unbounded: A348001(n) >= omega(n).

a(31) > 2*10^10.

Links

Table of n, a(n) for n=1..30.

Example

The first 12 terms of A348001(k) are 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2 and 4. The record values, 1, 2 and 4, are obtained at k = 1, 3 and 12. Therefore, this sequence begins with 1, 3, 12.

Mathematica

f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := Length @ Union[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; sm = 0; seq = {}; Do[s1 = s[n]; If[s1 > sm, sm = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq

Crossrefs

The unitary version of A328858.

Cf. A047994, A348001, A348003.

Sequence in context: A159867 A082278 A078162 * A211774 A002497 A228251

Adjacent sequences: A347999 A348000 A348001 * A348003 A348004 A348005

Keyword

nonn,more

Author

Amiram Eldar, Sep 23 2021

Status

approved