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

1,2

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

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 *)

Crossrefs

Subsequence of A025487.

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

Sequence in context: A358513 A004653 A115386 * A058771 A358512 A036493

Adjacent sequences: A306488 A306489 A306490 * A306492 A306493 A306494

Keyword

nonn

Author

Amiram Eldar, Feb 19 2019

Status

approved