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

1,10

Links

Table of n, a(n) for n=1..86.

Index entries for sequences related to partitions

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).

Example

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.

Crossrefs

Cf. A356609.

Sequence in context: A121814 A195298 A010581 * A276987 A348510 A200489

Adjacent sequences: A356917 A356918 A356919 * A356921 A356922 A356923

Keyword

nonn

Author

Wesley Ivan Hurt, Sep 04 2022

Status

approved