A356919 Number of partitions of n into 5 parts that divide n.

0, 0, 0, 0, 1, 1, 0, 2, 1, 2, 0, 8, 0, 1, 3, 3, 0, 6, 0, 6, 1, 0, 0, 20, 1, 0, 1, 2, 0, 14, 0, 3, 0, 0, 1, 20, 0, 0, 0, 11, 0, 8, 0, 0, 5, 0, 0, 26, 0, 2, 0, 0, 0, 7, 1, 4, 0, 0, 0, 41, 0, 0, 2, 3, 1, 2, 0, 0, 0, 5, 0, 35, 0, 0, 3, 0, 0, 2, 0, 12, 1, 0, 0, 25, 1, 0, 0, 2, 0, 23, 0, 0, 0, 0, 1, 27, 0, 1, 1, 7, 0, 1, 0, 2, 4

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to partitions

Formula

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

Example

a(12) = 8; there are 8 ways to write 12 as the sum of 5 divisors of 12: 6+3+1+1+1 = 6+2+2+1+1 = 4+4+2+1+1 = 4+3+3+1+1 = 4+3+2+2+1 = 4+2+2+2+2 = 3+3+3+2+1 = 3+3+2+2+2.

Prog

(PARI) A356919(n, x=n, y=n, nparts=5) = if(0==nparts, (0==y), if(y<=0, 0, sumdiv(n, d, if((d<=x), A356919(n, d, y-d, nparts-1))))); \\ Antti Karttunen, Jan 13 2025

Crossrefs

Cf. A355641.

Sequence in context: A197522 A121310 A379781 * A278158 A218880 A024356

Adjacent sequences: A356916 A356917 A356918 * A356920 A356921 A356922

Keyword

nonn

Author

Wesley Ivan Hurt, Sep 04 2022

Extensions

More terms from Antti Karttunen, Jan 13 2025

Status

approved