A356920 Number of partitions of n into 6 parts that divide n.

0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 8, 0, 1, 0, 4, 0, 8, 0, 8, 0, 0, 0, 33, 0, 0, 0, 6, 0, 27, 0, 5, 0, 0, 0, 44, 0, 0, 0, 21, 0, 16, 0, 1, 0, 0, 0, 61, 0, 3, 0, 1, 0, 13, 0, 11, 0, 0, 0, 124, 0, 0, 0, 5, 0, 6, 0, 0, 0, 8, 0, 104, 0, 0, 0, 0, 0, 5, 0, 31, 0, 0, 0, 77, 0, 0

Offset: 1

Author

Wesley Ivan Hurt, Sep 04 2022

Keywords

• nonn

Examples

			a(12) = 8; there are 8 ways to write 12 as the sum of 6 divisors of 12: 6+2+1+1+1+1 = 4+4+1+1+1+1 = 4+3+2+1+1+1 = 4+2+2+2+1+1 = 3+3+3+1+1+1 = 3+3+2+2+1+1 = 3+2+2+2+2+1 = 2+2+2+2+2+2.
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A356609.

Formula

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(n/m) * c(n/l) * c(n/k) * c(n/j) * c(n/i) * c(n/(n-i-j-k-l-m)), where c(n) = 1 - ceiling(n) + floor(n).