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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.

%I A213208 #32 Oct 27 2023 21:14:47
%S A213208 1,1,1,3,5,9,11,19,23,33,39,51,57,75,87,103,117,143,155,187,207,235,
%T A213208 259,297,319,363,395,441,473,525,555,615,659,721,765,831,875,959,1017,
%U A213208 1091,1147,1239,1291,1397,1467,1553,1631,1743,1813,1937,2023,2141,2233,2379,2465
%N 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.
%C A213208 This sequence is in reply to an extension request made in A100450.
%C A213208 Note that gcd(0,m) = m for any m.
%H A213208 Alois P. Heinz, <a href="/A213208/b213208.txt">Table of n, a(n) for n = 0..1000</a> (terms n = 0..100 from Robert Price)
%p A213208 h:= proc() true end:
%p A213208 b:= proc(n) local c, i, j, p;
%p A213208       c:=0;
%p A213208       for i to iquo(n, 3) do
%p A213208         for j from i to iquo(n-i, 2) do
%p A213208           if igcd(i, j, n-i-j)=1 then p:= i*j*(n-i-j);
%p A213208             if h(p) then h(p):= false; c:=c+1 fi
%p A213208           fi
%p A213208         od
%p A213208       od; c
%p A213208     end:
%p A213208 a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +2*b(n)) end:
%p A213208 seq(a(n), n=0..60);  # _Alois P. Heinz_, Mar 01 2013
%t A213208 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}]
%Y A213208 Cf. A018805, A027430, A100448, A100449, A100450, A213207, A213212, A213213.
%K A213208 nonn,easy
%O A213208 0,4
%A A213208 _Robert Price_, Mar 01 2013