A306491 - OEIS

%I #27 Aug 23 2024 21:03:07

%S 1,2,4,8,12,24,48,96,144,192,288,480,576,720,1152,1440,2880,4320,5760,

%T 8640,11520,17280,34560,51840,69120,103680,120960,138240,207360,

%U 241920,345600,362880,414720,483840,604800,725760,829440,967680,1209600,1451520,1814400

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

%C 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).

%C Numbers that set a record for the number of divisors of least prime signature (A322584). - _Hal M. Switkay_, Aug 20 2024

%H Amiram Eldar, <a href="/A306491/b306491.txt">Table of n, a(n) for n = 1..533</a>

%H Amiram Eldar, <a href="/A306491/a306491_1.txt">Table of n, a(n), A085082(a(n)) for n = 1..533</a>

%t 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 *)

%Y Subsequence of A025487.

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Feb 19 2019