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%I #10 Dec 12 2020 14:19:25
%S 0,0,0,1,1,2,3,4,5,7,8,10,12,12,12,19,19,22,27,28,31,31,38,42,46,50,
%T 50,57,51,64,71,70,77,85,86,84,104,104,108,108,123,122,119,136,147,
%U 158,156,164,170,162,194,195,193,205,219,228,215,233,254,254,278
%N Number of distinct integers that are product of the parts of exactly one partition of n into 3 positive parts.
%H Alois P. Heinz, <a href="/A306435/b306435.txt">Table of n, a(n) for n = 0..10000</a>
%p a:= proc(n) option remember; local m, c, i, j, h, w;
%p m, c:= proc() 0 end, 0; forget(m);
%p for i to iquo(n, 3) do for j from i to iquo(n-i, 2) do
%p h:= i*j*(n-j-i); w:= m(h);
%p if w=0 then m(h):= 1; c:= c+1
%p elif w=1 then m(h):= 2; c:= c-1
%p fi
%p od od; c
%p end:
%p seq(a(n), n=0..80);
%t a[n_] := a[n] = Module[{m, c = 0, i, j, h, w}, m[_] = 0; For[i = 1, i <= Quotient[n, 3], i++, For[j = i, j <= Quotient[n-i, 2], j++, h = i*j*(n - j - i); w = m[h]; If[w==0, m[h] = 1; c++; If[w==1, m[h] = 2; c--]]]]; c];
%t a /@ Range[0, 80] (* _Jean-François Alcover_, Dec 12 2020, after _Alois P. Heinz_ *)
%Y Column k=1 of A317578.
%K nonn
%O 0,6
%A _Alois P. Heinz_, Feb 15 2019
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