%I #22 Apr 10 2019 12:24:27

%S -25,-8,-3,0,24,27,32,49

%N Numbers k such that k = i*j = 6*i + j, where i and j are integers

%C The sequence can be found by solving the equality i*j = 6*i + j. Re-arranging for j gives j = 6 + 6/(i-1). As both i and j must be integers this implies i - 1 must divide 6, thus the only values for i are -5,-2,-1,0,2,3,4,7. Finding the corresponding j and multiplying gives the 8 sequences values.

%C In general if we replace 6 by n, then the number of solutions will be 2*A000005(n), the lowest value will be -(n - 1)^2, and the highest value will be (n + 1)^2.

%C For values k>=0 this sequence gives the possible point scores in Australian Rules Football which equal the corresponding number of goals (worth six points) times the number of behinds (worth one point).

%C The number of solutions, in this case 8, is given by A062011(6). _Robert G. Wilson v_, Apr 10 2019

%e The 8 solutions are:

%e --------------

%e i j k

%e --------------

%e -5 5 -25

%e -2 4 -8

%e -1 3 -3

%e 0 0 0

%e 2 12 24

%e 3 9 27

%e 4 8 32

%e 7 7 49

%Y Cf. A000005

%K sign,fini,full

%O 1,1

%A _Scott R. Shannon_, Mar 27 2019