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%I A307179 #22 Apr 10 2019 12:24:27
%S A307179 -25,-8,-3,0,24,27,32,49
%N A307179 Numbers k such that k = i*j = 6*i + j, where i and j are integers
%C A307179 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 A307179 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 A307179 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 A307179 The number of solutions, in this case 8, is given by A062011(6). _Robert G. Wilson v_, Apr 10 2019
%e A307179 The 8 solutions are:
%e A307179 --------------
%e A307179 i   j    k
%e A307179 --------------
%e A307179 -5   5   -25
%e A307179 -2   4   -8
%e A307179 -1   3   -3
%e A307179 0   0    0
%e A307179 2   12   24
%e A307179 3   9    27
%e A307179 4   8    32
%e A307179 7   7    49
%Y A307179 Cf. A000005
%K A307179 sign,fini,full
%O A307179 1,1
%A A307179 _Scott R. Shannon_, Mar 27 2019

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