A182854 Integers whose prime signature a) contains at least two distinct numbers, and b) contains no number that occurs less often than any other number.

12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 63, 68, 72, 75, 76, 80, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 124, 135, 136, 144, 147, 148, 152, 153, 160, 162, 164, 171, 172, 175, 176, 184, 188, 189, 192, 200, 207, 208, 212, 224, 232, 236, 242, 244, 245

Offset: 1

Author

Matthew Vandermast, Jan 04 2011

Keywords

• nonn

Comments

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.

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).

Examples

			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.
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).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Fixed Point
• Eric Weisstein's World of Mathematics, Map

Crossrefs

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

Subsequence of A059404 and A182852.

Programs

Mathematica

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