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a(n) = b(2n-1)*b(2n) where b(3n+1) = floor(n/9) + 2, b(3n+2) = (n mod 9) + 2, b(3n+3) = b(3n+1)*b(3n+2) for n >= 0.
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%I #15 Nov 01 2022 18:17:26

%S 4,8,18,8,16,50,12,24,98,16,32,162,20,60,12,9,27,48,15,45,108,21,63,

%T 192,27,81,300,8,32,36,16,64,100,24,96,196,32,128,324,40,200,20,15,75,

%U 80,25,125,180,35,175,320,45,225,500,12,72,54,24,144,150,36,216,294,48,288

%N a(n) = b(2n-1)*b(2n) where b(3n+1) = floor(n/9) + 2, b(3n+2) = (n mod 9) + 2, b(3n+3) = b(3n+1)*b(3n+2) for n >= 0.

%C Old name was: (2*2=4, 2*3=6, 2*4=8, 2*5=10, 2*6=12, 2*7=14, 2*8=16, 2*9=18, 2*10=20, 3*2=6, ...) becomes (abs(2*2, 4*2, 3*6, 2*4, 8*2, 5*10, 2*6, 12*2, 7*14, 2*8, 16*2, 9*18, 2*10, 20*3, 2*6, ...)).

%C (..., 9*9=81, 9*10=90, 10*2=20, 10*3=30, 10*4=40, 10*5=50, 10*6=60, 10*7=70, 10*8=80, 10*9=90, 10*10=100, 11*2=22, ...) becomes

%C (abs(..., 9*9, 81*9, 10*90, 10*2, 20*10, 3*30, 10*4, 40*10, 5*50, 10*6, 60*10, 7*70, 10*8, 80*10, 9*90, 10*10, 100*11, 2*22, ...)).

%e 2*2 = 4 = a(1),

%e 4*2 = 8 = a(2),

%e 3*6 = 18 = a(3),

%e 2*4 = 8 = a(4),

%e 8*2 = 16 = a(5),

%e 5*10 = 50 = a(6), etc.

%t Times @@@ Partition[Flatten@ Table[{n, k, n k}, {n, 2, 10}, {k, 2, 10}], 2, 2] (* _Michael De Vlieger_, Oct 24 2022 *)

%o (PARI) a(n) = my(k=ceil(n/27), r=n-27*(k-1), v=[]); for(i=2, 10, v=concat(v,[2*k,i,2*k*i])); for(i=2, 10, v=concat(v,[2*k+1,i,(2*k+1)*i])); v[2*r-1] * v[2*r] \\ _Jianing Song_, Oct 24 2022

%Y Cf. A144176, A144177.

%K nonn,less

%O 1,1

%A _Juri-Stepan Gerasimov_, Nov 19 2008

%E Corrected (a 175 replaced by 225) by _R. J. Mathar_, Apr 29 2010

%E New name from _Jianing Song_, Nov 01 2022