%I #9 Aug 08 2019 04:36:00

%S 12,18,20,24,28,40,44,45,48,50,52,54,56,63,68,72,75,76,80,88,92,96,98,

%T 99,104,108,112,116,117,124,135,136,144,147,148,152,153,160,162,164,

%U 171,172,175,176,184,188,189,192,200,207,208,212,224,232,236,242,244,245

%N Integers whose prime signature a) contains at least two distinct numbers, and b) contains no number that occurs less often than any other number.

%C Numbers that require exactly four iterations to reach a fixed point under the x -> A181819(x) map. In each case, 2 is the fixed point that is reached. (1 is the other fixed point of the x -> A181819(x) map.) Cf. A182850.

%C Not the same sequence as A177425, which is a proper subsequence. 1260 is the first nonmember of A177425 that belongs to this sequence; its prime signature is (2,2,1,1).

%H Amiram Eldar, <a href="/A182854/b182854.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FixedPoint.html">Fixed Point</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Map.html">Map</a>

%e The prime signature of 12 (2^2*3^1) is (2,1). Since (2,1) contains at least two distinct numbers, and since each number that appears in (2,1) appears exactly as often as any other number that appears, 12 belongs to this sequence.

%e 12 also requires exactly four iterations under the x -> A181819(x) map to reach a fixed point (namely, 2) . A181819(12) = 6; A181819(6) = 4; A181819(4) = 3; A181819(3) = 2 (and A181819(2) = 2).

%t aQ[n_] := Length[v = Values @ Counts @ FactorInteger[n][[;;,2]]] > 1 && Length @ Union @ v == 1; Select[Range[250], aQ] (* _Amiram Eldar_, Aug 08 2019 *)

%Y Numbers n such that A182850(n) = 4. See also A182853, A182855.

%Y Subsequence of A059404 and A182852.

%K nonn

%O 1,1

%A _Matthew Vandermast_, Jan 04 2011