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%I #20 Sep 26 2022 20:36:08
%S 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,
%T 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,
%U 0,1,0,10,0,0,0,1,0,2,0,4,0,0,0,8,0,0,0,2,0,5
%N Number of partitions of n into 4 parts that divide n.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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).
%e 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.
%Y Cf. A354591.
%K nonn
%O 1,6
%A _Wesley Ivan Hurt_, Sep 04 2022
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