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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A025487, A087980, A002182.

Sequence in context: A369958 A197880 A175497 * A282944 A188062 A056153

Adjacent sequences: A161809 A161810 A161811 * A161813 A161814 A161815

Keyword

easy,nonn

Author

Peter Luschny, Jun 20 2009

Extensions

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

Status

approved