A213208 Number of distinct products i*j*k over all triples (i,j,k) with |i| + |j| + |k| <= n and gcd(i,j,k) <= 1.

1, 1, 1, 3, 5, 9, 11, 19, 23, 33, 39, 51, 57, 75, 87, 103, 117, 143, 155, 187, 207, 235, 259, 297, 319, 363, 395, 441, 473, 525, 555, 615, 659, 721, 765, 831, 875, 959, 1017, 1091, 1147, 1239, 1291, 1397, 1467, 1553, 1631, 1743, 1813, 1937, 2023, 2141, 2233, 2379, 2465

Offset: 0

Author

Robert Price, Mar 01 2013

Keywords

• nonn
• easy

Comments

This sequence is in reply to an extension request made in A100450.

Note that gcd(0,m) = m for any m.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 0..100 from Robert Price)

Crossrefs

Cf. A018805, A027430, A100448, A100449, A100450, A213207, A213212, A213213.

Programs

Maple

h:= proc() true end:
b:= proc(n) local c, i, j, p;
      c:=0;
      for i to iquo(n, 3) do
        for j from i to iquo(n-i, 2) do
          if igcd(i, j, n-i-j)=1 then p:= i*j*(n-i-j);
            if h(p) then h(p):= false; c:=c+1 fi
          fi
        od
      od; c
    end:
a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +2*b(n)) end:
seq(a(n), n=0..60);  # Alois P. Heinz, Mar 01 2013

Mathematica

f[n_] := Length[ Union[ Flatten[ Table[ If[ Abs[i] + Abs[j] + Abs[k] <= n&& GCD[i, j, k] <= 1, i*j*k, 0], {i, -n, n}, {j, -n, n}, {k, -n, n}], 2]]]; Table[ f[n], {n, 0, 100}]