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Number of ways to write n as a product with all factors <= n/3.
8

%I #8 Jul 13 2013 12:04:31

%S 0,0,0,0,0,0,0,1,1,0,0,2,0,0,1,3,0,2,0,2,1,0,0,5,1,0,2,2,0,3,0,5,1,0,

%T 1,7,0,0,1,5,0,3,0,2,3,0,0,10,1,2,1,2,0,5,1,5,1,0,0,9,0,0,3,9,1,3,0,2,

%U 1,3,0,14,0,0,3,2,1,3,0,10,4,0,0,9,1

%N Number of ways to write n as a product with all factors <= n/3.

%C a(n) = A066032(n,floor(n/3)) for n > 2.

%H Reinhard Zumkeller, <a href="/A216599/b216599.txt">Table of n, a(n) for n = 1..1000</a>

%e a(30) = #{10*3, 6*5, 5*3*2} = 3;

%e a(31) = #{} = 0;

%e a(32) = #{8*4, 8*2*2, 4*4*2, 4*2*2*2, 2*2*2*2*2} = 5;

%e a(33) = #{11*3} = 1;

%e a(34) = #{} = 0;

%e a(35) = #{7*5} = 1;

%e a(36) = #{12*3, 9*4, 9*2*2, 6*6, 6*3*2, 4*3*3, 3*3*2*2} = 7.

%o (Haskell)

%o a216599 n | n <= 2 = 0

%o | otherwise = a066032_tabl !! (n-1) !! (n `div` 3 - 1)

%Y Cf. A001055, A028422, A216600, A216601, A216602.

%K nonn

%O 1,12

%A _Reinhard Zumkeller_, Oct 01 2012