A223135 Number of distinct sums i + j + k with i, j, k >= 0, i*j*k = n and gcd(i,j,k) <= 1.

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, 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, 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

Offset: 0

Author

Robert Price, Jun 12 2013

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10001 (terms n = 0..100 from Robert Price)

Crossrefs

Cf. A226357, A226359, A222945, A222947, A223133, A223134, A226378.

Programs

Mathematica

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}]

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

Extensions

More terms from Antti Karttunen, Oct 21 2017