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A343270 Number of partitions of n into 3 parts x,y,z such that (x+y+z) | x*y*z.

%I A343270 #5 Apr 10 2021 22:40:01
%S A343270 0,0,0,0,0,1,0,1,1,2,0,3,0,3,4,5,0,6,0,6,6,5,0,11,2,6,7,9,0,23,0,11,
%T A343270 10,8,12,15,0,9,12,21,0,34,0,15,19,11,0,41,4,18,16,18,0,36,20,31,18,
%U A343270 14,0,61,0,15,28,33,24,56,0,24,22,65,0,48,0,18,32,27,30,67,0,77
%N A343270 Number of partitions of n into 3 parts x,y,z such that (x+y+z) | x*y*z.
%H A343270 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A343270 a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(i*j*(n-i-j)/n) + floor(i*j*(n-i-j)/n)).
%e A343270 a(9) = 1; [3,3,3];
%e A343270 a(10) = 2; [1,4,5], [2,3,5];
%e A343270 a(11) = 0;
%e A343270 a(12) = 3; [1,3,8], [2,4,6], [3,4,5].
%t A343270 Table[Sum[Sum[(1 - Ceiling[i*j*(n - i - j)/n] + Floor[i*j*(n - i - j)/n]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]
%K A343270 nonn
%O A343270 1,10
%A A343270 _Wesley Ivan Hurt_, Apr 09 2021