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A227800 Number of different values the product p*q can have where p >= 1, q >= 1 with p+q < n.

%I A227800 #26 Sep 23 2024 11:58:55
%S A227800 0,0,1,2,4,5,8,10,13,16,19,21,26,29,34,39,44,48,53,58,65,71,78,83,91,
%T A227800 97,104,111,118,124,134,141,150,158,167,176,186,194,204,213,224,232,
%U A227800 245,254,267,278,290,301,315,328,339,351,366,376,391,404,419,432,446
%N A227800 Number of different values the product p*q can have where p >= 1, q >= 1 with p+q < n.
%C A227800 Game played often with n = 10.
%H A227800 Alois P. Heinz, <a href="/A227800/b227800.txt">Table of n, a(n) for n = 1..2000</a>
%H A227800 Cristina Ballantine, George Beck, Mircea Merca, and Bruce Sagan, <a href="https://arxiv.org/abs/2409.11268">Elementary symmetric partitions</a>, arXiv:2409.11268 [math.CO], 2024. See p. 20.
%p A227800 A227800 := proc(n)
%p A227800     local s, p, q ;
%p A227800     s := {} ;
%p A227800     for p from 1 to iquo(n-1, 2) do
%p A227800     for q from p to n-1-p do
%p A227800             s := s union {p*q} ;
%p A227800     end do:
%p A227800     end do:
%p A227800     nops(s) ;
%p A227800 end proc:
%p A227800 seq(A227800(n), n=1..120) ; # _R. J. Mathar_, Nov 24 2013
%t A227800 A227800[n_] := Module[{s, p, q}, s = {}; For[p = 1, p <= Quotient[n-1, 2], p++, For[q = p, q <= n-1-p, q++, s = s ~Union~ {p*q}]] ; Length[s]]; Table[A227800[n], {n, 1, 120}] (* _Jean-François Alcover_, Feb 27 2014, after _R. J. Mathar_ *)
%K A227800 nonn
%O A227800 1,4
%A A227800 _Henry W. Gould_, Sep 23 2013