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%I #28 Aug 02 2019 03:43:01
%S 1,1,1,1,2,1,2,1,2,2,2,1,4,1,2,2,3,1,4,1,4,2,2,1,5,2,2,2,4,1,5,1,3,2,
%T 2,2,7,1,2,2,5,1,5,1,4,4,2,1,7,2,4,2,4,1,5,2,5,2,2,1,10,1,2,4,4,2,5,1,
%U 4,2,5,1,10,1,2,4,4,2,5,1,7,3,2,1,10,2,2,2,5,1,8,2,4,2,2,2,7,1,4,4,8,1,5,1,5,5
%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 Antti Karttunen, <a href="/A223135/b223135.txt">Table of n, a(n) for n = 0..10001</a> (terms n = 0..100 from Robert Price)
%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}]
%o (PARI) A223135(n) = { my(sums=Set()); if(!n,1,fordiv(n, i, for(j=i, (n/i), if(!(n%j),for(k=j, n/(i*j), if((i*j*k==n)&&(gcd(i,gcd(j,k))<=1), sums = Set(concat(sums, (i+j+k)))))))); length(sums)); }; \\ _Antti Karttunen_, Oct 21 2017
%Y Cf. A226357, A226359, A222945, A222947, A223133, A223134, A226378.
%K nonn
%O 0,5
%A _Robert Price_, Jun 12 2013
%E More terms from _Antti Karttunen_, Oct 21 2017
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