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

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, 97, 104, 111, 118, 124, 134, 141, 150, 158, 167, 176, 186, 194, 204, 213, 224, 232, 245, 254, 267, 278, 290, 301, 315, 328, 339, 351, 366, 376, 391, 404, 419, 432, 446

Offset: 1

Author

Henry W. Gould, Sep 23 2013

Keywords

• nonn

Comments

Game played often with n = 10.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000
• Cristina Ballantine, George Beck, Mircea Merca, and Bruce Sagan, Elementary symmetric partitions, arXiv:2409.11268 [math.CO], 2024. See p. 20.

Programs

Maple

A227800 := proc(n)
    local s, p, q ;
    s := {} ;
    for p from 1 to iquo(n-1, 2) do
    for q from p to n-1-p do
            s := s union {p*q} ;
    end do:
    end do:
    nops(s) ;
end proc:
seq(A227800(n), n=1..120) ; # R. J. Mathar, Nov 24 2013

Mathematica

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 *)