A169644 - OEIS

%I #7 Oct 22 2024 18:34:14

%S 72,120,144,180,240,252,288,336,360,378,400,420,432,450,480,504,540,

%T 576,594,600,630,648,660,672,700,720,756,780,792,800,840,858,864,900,

%U 924,936,960,1008,1050,1056,1080,1092,1120,1152,1170,1188,1200,1225,1248

%N Numbers with two or more distinct factorizations m*k such that m <= k <= 2*m.

%C Numbers n such that A067742(n) >= 3.

%C The smallest number with 3 such factorizations is 840 = 28*30 = 24*35 = 21*40.

%H Robert Israel, <a href="/A169644/b169644.txt">Table of n, a(n) for n = 1..10000</a>

%e 72 = 8 * 9 = 6 * 12, so it is in the sequence. 60 = 6 * 10, but the next closest factorization is 5 * 12 and 12 > 2*5, so 60 is not in the sequence.

%p filter:= proc(n) nops(select(t -> t^2 >= n/2 and t^2 <= 2*n, numtheory:-divisors(n)))>=3 end proc:

%p select(filter, [$1..2000]); # _Robert Israel_, Oct 21 2024

%Y Cf. A067742, A071562, A100345.

%K nonn

%O 1,1

%A _Franklin T. Adams-Watters_, Apr 04 2010