Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Apr 11 2021 23:40:18
%S 0,0,0,0,0,1,0,0,0,2,0,3,0,3,4,2,0,4,0,6,6,5,0,10,0,6,3,9,0,23,0,8,10,
%T 8,12,13,0,9,12,20,0,34,0,15,18,11,0,38,1,14,16,18,0,28,20,30,18,14,0,
%U 61,0,15,27,26,24,56,0,24,22,65,0,43,0,18,30,27,30,67,0,74
%N Number of partitions of n into 3 distinct parts x,y,z such that (x+y+z) | x*y*z.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F 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)) * (1 - [i = j]) * (1 - [n-i = 2*j]) * (1 - [n-j = 2*i]), where [ ] is the Iverson bracket.
%e a(10) = 2; [1,4,5], [2,3,5], with all parts distinct;
%e a(12) = 3; [1,3,8], [2,4,6], [3,4,5], with all parts distinct.
%t Table[Sum[Sum[(1 - KroneckerDelta[i, j]) (1 - KroneckerDelta[n - j, 2 i]) (1 - KroneckerDelta[n - i, 2 j]) (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}]
%Y Cf. A343270.
%K nonn
%O 1,10
%A _Wesley Ivan Hurt_, Apr 11 2021