A213208 - OEIS

%I #32 Oct 27 2023 21:14:47

%S 1,1,1,3,5,9,11,19,23,33,39,51,57,75,87,103,117,143,155,187,207,235,

%T 259,297,319,363,395,441,473,525,555,615,659,721,765,831,875,959,1017,

%U 1091,1147,1239,1291,1397,1467,1553,1631,1743,1813,1937,2023,2141,2233,2379,2465

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

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

%H 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 h:= proc() true end:

%p b:= proc(n) local c, i, j, p;

%p       c:=0;

%p       for i to iquo(n, 3) do

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

%p           if igcd(i, j, n-i-j)=1 then p:= i*j*(n-i-j);

%p             if h(p) then h(p):= false; c:=c+1 fi

%p           fi

%p         od

%p       od; c

%p     end:

%p a:= proc(n) a(n):= `if`(n=0, 1, a(n-1) +2*b(n)) end:

%p seq(a(n), n=0..60);  # _Alois P. Heinz_, Mar 01 2013

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

%K nonn,easy

%O 0,4

%A _Robert Price_, Mar 01 2013