A356915 Number of partitions of n into 4 parts that divide n.

0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 7, 0, 0, 0, 2, 0, 3, 0, 3, 0, 0, 0, 9, 0, 0, 0, 1, 0, 4, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 3, 0, 1, 0, 0, 0, 9, 0, 1, 0, 1, 0, 3, 0, 2, 0, 0, 0, 10, 0, 0, 0, 2, 0, 2, 0, 1, 0, 1, 0, 10, 0, 0, 0, 1, 0, 2, 0, 4, 0, 0, 0, 8, 0, 0, 0, 2, 0, 5

Offset

1,6

Links

Table of n, a(n) for n=1..90.

Index entries for sequences related to partitions

Formula

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

Example

a(12) = 7; there are 7 ways to write 12 as the sum of 4 divisors of 12: 6+4+1+1 = 6+3+2+1 = 6+2+2+2 = 4+4+3+1 = 4+4+2+2 = 4+3+3+2 = 3+3+3+3.

Crossrefs

Cf. A354591.

Sequence in context: A328766 A219203 A341981 * A226786 A266330 A320313

Adjacent sequences: A356912 A356913 A356914 * A356916 A356917 A356918

Keyword

nonn

Author

Wesley Ivan Hurt, Sep 04 2022

Status

approved