A306491 Numbers that set a record for the number of distinct prime signatures represented among their divisors (A085082).

1, 2, 4, 8, 12, 24, 48, 96, 144, 192, 288, 480, 576, 720, 1152, 1440, 2880, 4320, 5760, 8640, 11520, 17280, 34560, 51840, 69120, 103680, 120960, 138240, 207360, 241920, 345600, 362880, 414720, 483840, 604800, 725760, 829440, 967680, 1209600, 1451520, 1814400

Offset: 1

Author

Amiram Eldar, Feb 19 2019

Keywords

• nonn

Comments

The records are 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 15, 16, 18, 19, 21, 24, 29, 30, 34, 37, 39, 44, 51, 52, 58, 61, 62, 65, 70, ... (see the link for more values).

Numbers that set a record for the number of divisors of least prime signature (A322584). - Hal M. Switkay, Aug 20 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..533
• Amiram Eldar, Table of n, a(n), A085082(a(n)) for n = 1..533

Crossrefs

Subsequence of A025487.

Cf. A085082, A182860, A182862 (unitary version), A322584.

Programs

Mathematica

ps[1] = {}; ps[n_] := FactorInteger[n][[All, 2]] // Sort; a[n_] := ps /@ Divisors[n] // Union // Length; s={}; am=0; Do[a1=a[n]; If[a1>am, am=a1; AppendTo[s, n]], {n, 1, 2*10^6}]; s (* after Jean-François Alcover at A085082 *)