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%I #16 Feb 24 2020 08:57:59
%S 0,0,0,1,1,2,3,4,5,7,8,10,12,13,14,19,20,23,27,29,32,34,39,43,47,51,
%T 53,59,58,67,73,75,81,88,91,93,106,109,114,117,128,131,133,145,154,
%U 163,166,174,181,180,201,206,209,219,231,240,238,252,267,272,289,290,300,299,323,328,345,349,366,376
%N The number of distinct products that can be formed by multiplying the parts of a partition of n into 3 positive parts.
%H Alois P. Heinz, <a href="/A306403/b306403.txt">Table of n, a(n) for n = 0..10000</a>
%H R. J. Mathar, <a href="/A306403/a306403.java.txt">Java program that computes a b-file</a>
%F a(n) <= A069905(n).
%p a:= proc(n) option remember; local m, c, i, j, h, w;
%p m, c:= proc() true 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 then m(h):= false; c:= c+1 fi
%p od od; c
%p end:
%p seq(a(n), n=0..80); # _Alois P. Heinz_, Feb 13 2019
%t a[n_] := a[n] = Module[{m, c = 0, i, j, h, w}, m[_] = True; 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, m[h] = False; c++]]]; c];
%t a /@ Range[0, 80] (* _Jean-François Alcover_, Feb 24 2020, after _Alois P. Heinz_ *)
%Y Row sums of A317578.
%Y Cf. A069905.
%K nonn
%O 0,6
%A _R. J. Mathar_, Feb 13 2019
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