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

%I #26 Sep 23 2024 11:58:55

%S 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 97,104,111,118,124,134,141,150,158,167,176,186,194,204,213,224,232,

%U 245,254,267,278,290,301,315,328,339,351,366,376,391,404,419,432,446

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

%C Game played often with n = 10.

%H Alois P. Heinz, <a href="/A227800/b227800.txt">Table of n, a(n) for n = 1..2000</a>

%H 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 := proc(n)

%p local s, p, q ;

%p s := {} ;

%p for p from 1 to iquo(n-1, 2) do

%p for q from p to n-1-p do

%p s := s union {p*q} ;

%p end do:

%p end do:

%p nops(s) ;

%p end proc:

%p seq(A227800(n), n=1..120) ; # _R. J. Mathar_, Nov 24 2013

%t 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 nonn

%O 1,4

%A _Henry W. Gould_, Sep 23 2013