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

0,9

Comments

a(n) <= A023895(n).

Links

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

Example

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;

Crossrefs

Sequence in context: A240205 A340732 A050319 * A257873 A229817 A080966

Adjacent sequences: A132453 A132454 A132455 * A132457 A132458 A132459

Keyword

nonn

Author

Reinhard Zumkeller, Aug 22 2007

Status

approved