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%I #7 Sep 26 2022 20:36:27
%S 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,
%T 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,
%U 5,0,6,0,0,0,8,0,104,0,0,0,0,0,5,0,31,0,0,0,77,0,0
%N Number of partitions of n into 6 parts that divide n.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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).
%e 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.
%Y Cf. A356609.
%K nonn
%O 1,10
%A _Wesley Ivan Hurt_, Sep 04 2022
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