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A307179
Numbers k such that k = i*j = 6*i + j, where i and j are integers
0
-25, -8, -3, 0, 24, 27, 32, 49
OFFSET
1,1
COMMENTS
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.
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.
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).
The number of solutions, in this case 8, is given by A062011(6). Robert G. Wilson v, Apr 10 2019
EXAMPLE
The 8 solutions are:
--------------
i j k
--------------
-5 5 -25
-2 4 -8
-1 3 -3
0 0 0
2 12 24
3 9 27
4 8 32
7 7 49
CROSSREFS
Sequence in context: A248583 A080203 A040605 * A065910 A096521 A215539
KEYWORD
sign,fini,full
AUTHOR
Scott R. Shannon, Mar 27 2019
STATUS
approved