login
Number of solutions to n = x + y + z in positive integers x,y,z such that (x+y) does not divide any of x*y, y*z, or x*z.
0

%I #9 Apr 09 2021 09:31:15

%S 0,0,1,1,1,2,3,4,5,5,7,9,10,12,16,17,18,21,23,27,30,33,36,41,43,45,50,

%T 54,57,63,67,72,76,81,88,93,96,102,110,117,121,130,135,143,151,155,

%U 163,173,177,182,190,198,205,215,224,233,240,249,259,272,278,288,301,308,317

%N Number of solutions to n = x + y + z in positive integers x,y,z such that (x+y) does not divide any of x*y, y*z, or x*z.

%F a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (ceiling(i*j/(i+j)) - floor(i*j/(i+j))) * (ceiling((i*(n-i-j))/(n-j)) - floor(i*(n-i-j)/(n-j))) * (ceiling((j*(n-i-j))/(n-i)) - floor(j*(n-i-j)/(n-i))).

%t Table[Sum[Sum[(Ceiling[i*j/(i + j)] - Floor[i*j/(i + j)]) (Ceiling[(i*(n - i - j))/(n - j)] - Floor[i*(n - i - j)/(n - j)]) (Ceiling[(j*(n - i - j))/(n - i)] - Floor[j*(n - i - j)/(n - i)]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]

%Y Cf. A005279.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Apr 05 2021