A161812 Numbers with decreasing but not strictly decreasing prime signature.

6, 30, 36, 60, 120, 180, 210, 216, 240, 420, 480, 840, 900, 960, 1080, 1260, 1296, 1680, 1800, 1920, 2310, 2520, 3360, 3600, 3840, 4620, 5040, 5400, 6300, 6480, 6720, 7200, 7560, 7680, 7776, 9240, 10080, 12600, 13440, 13860, 14400, 15120, 15360, 18480

Offset: 1

Author

Peter Luschny, Jun 20 2009

Keywords

• easy
• nonn

Comments

All numbers of the form 2^k1*3^k2*...*p_n^k_n, where k1 >= k2 >= ... >= k_n, and the '=' occurs at least once, sorted.

It appears that all highly composite numbers (A002182) greater than 720 are in this sequence. - Walter Roscello, Dec 24 2013

Examples

			a(1) = 2*3, a(2) = 2*3*5, a(3) = 2^2*3^2, a(4) = 2^2*3*5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..279 from Walter Roscello)

Crossrefs

Cf. A025487, A087980, A002182.

Programs

Mathematica

okQ[n_] := Module[{pp, ee}, {pp, ee} = Transpose[FactorInteger[n]]; Length[pp] == PrimePi[pp // Last] && GreaterEqual @@ ee && Sort[ee] != Union[ee]]; Select[Range[20000], okQ] (* Jean-François Alcover, Jun 17 2019 *)

Extensions

Terms up to n=279 added by Walter Roscello, Dec 24 2013