login
A169644
Numbers with two or more distinct factorizations m*k such that m <= k <= 2*m.
1
72, 120, 144, 180, 240, 252, 288, 336, 360, 378, 400, 420, 432, 450, 480, 504, 540, 576, 594, 600, 630, 648, 660, 672, 700, 720, 756, 780, 792, 800, 840, 858, 864, 900, 924, 936, 960, 1008, 1050, 1056, 1080, 1092, 1120, 1152, 1170, 1188, 1200, 1225, 1248
OFFSET
1,1
COMMENTS
Numbers n such that A067742(n) >= 3.
The smallest number with 3 such factorizations is 840 = 28*30 = 24*35 = 21*40.
LINKS
EXAMPLE
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.
MAPLE
filter:= proc(n) nops(select(t -> t^2 >= n/2 and t^2 <= 2*n, numtheory:-divisors(n)))>=3 end proc:
select(filter, [$1..2000]); # Robert Israel, Oct 21 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved