This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356919 #15 Mar 10 2025 08:55:54
%S A356919 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,
%T A356919 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,
%U A356919 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
%N A356919 Number of partitions of n into 5 parts that divide n.
%H A356919 Antti Karttunen, <a href="/A356919/b356919.txt">Table of n, a(n) for n = 1..20000</a>
%H A356919 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A356919 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).
%e A356919 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.
%o A356919 (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
%Y A356919 Cf. A355641.
%K A356919 nonn
%O A356919 1,8
%A A356919 _Wesley Ivan Hurt_, Sep 04 2022
%E A356919 More terms from _Antti Karttunen_, Jan 13 2025