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

1,1

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).

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

Example

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).

Mathematica

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

Crossrefs

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

Subsequence of A059404 and A182852.

Sequence in context: A332785 A367589 A177425 * A348097 A345381 A328930

Adjacent sequences: A182851 A182852 A182853 * A182855 A182856 A182857

Keyword

nonn

Author

Matthew Vandermast, Jan 04 2011

Status

approved