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Number of distinct sums i+j+k with i,j,k >= 0, i*j*k <= n and gcd(i,j,k) <= 1.
5

%I #21 Aug 02 2019 03:42:57

%S 1,4,5,6,8,10,11,14,15,18,19,22,23,26,27,30,31,34,35,38,39,42,43,46,

%T 47,50,51,54,55,58,59,62,63,66,67,70,71,74,75,78,79,82,83,86,87,90,91,

%U 94,95,98,99,102,103,106,107,110,111,114,115,118,119,122,123

%N Number of distinct sums i+j+k with i,j,k >= 0, i*j*k <= n and gcd(i,j,k) <= 1.

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

%H Robert Price, <a href="/A223133/b223133.txt">Table of n, a(n) for n = 0..100</a>

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

%Y Cf. A226357, A226359, A222945, A222947.

%K nonn

%O 0,2

%A _Robert Price_, Jun 12 2013