A132456 Number of partitions of n into composite parts such that succeeding parts have a common prime factor.

1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 4, 0, 4, 2, 7, 0, 9, 1, 12, 4, 14, 1, 23, 4, 24, 9, 35, 3, 46, 7, 56, 18, 68, 14, 99, 16, 107, 36, 145, 24, 186, 39, 219, 72, 270, 56, 361, 84, 408, 134, 514, 117, 655, 173, 761, 244, 926, 238, 1194, 312, 1347, 458, 1669, 458, 2073, 588, 2389

Offset: 0

Author

Reinhard Zumkeller, Aug 22 2007

Keywords

• nonn

Comments

a(n) <= A023895(n).

Examples

			a(19) = #{9+6+4} = 1, A023895(19) = #{15+4, 10+9, 9+6+4} = 3;
a(20) = A023895(20) = 12;
a(21) = #{21, 15+6, 12+9, 9+6+6} = 4, A023895(21) = 6;
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000