A216599 Number of ways to write n as a product with all factors <= n/3.

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

Offset: 1

Author

Reinhard Zumkeller, Oct 01 2012

Keywords

• nonn

Comments

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

Examples

			a(30) = #{10*3, 6*5, 5*3*2} = 3;
a(31) = #{} = 0;
a(32) = #{8*4, 8*2*2, 4*4*2, 4*2*2*2, 2*2*2*2*2} = 5;
a(33) = #{11*3} = 1;
a(34) = #{} = 0;
a(35) = #{7*5} = 1;
a(36) = #{12*3, 9*4, 9*2*2, 6*6, 6*3*2, 4*3*3, 3*3*2*2} = 7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Haskell

a216599 n | n <= 2    = 0
          | otherwise = a066032_tabl !! (n-1) !! (n `div` 3 - 1)