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%I #4 Oct 29 2023 22:10:39
%S 9,28,52,57,73,89,124,129,129,168,172,177,192,201,228,289,289,292,313,
%T 339,345,364,393,408,409,432,444,456,480,504,513,513,520,568,577,577,
%U 577,579,616,628,649,649,696,705,724,744,753,784,801,844,883,889,921,952,964,969,969,984
%N Minimal values of a corresponding to the numbers c listed in A366862, i.e., such that there exist integers a > b > c such that ab+c, ac+b and bc+a are perfect squares.
%e a(1) = 9 since (a, b, c) = (9, 7, 1) is the smallest solution with c = A366862(1) = 1: 9*7 + 1 = 64, 9*1 + 7 = 16 = 7*1 + 9 are squares.
%e a(2) = 28 is in the sequence since (a, b, c) = (28, 9, 4) is the smallest solution with c = A366862(2) = 4.
%e a(3) = 52 is in the sequence since (a, b, c) = (52, 16, 9) is the smallest solution with c = A366862(3) = 9.
%e a(4) = 16 is in the sequence since (a, b, c) = (57, 49, 16) is the smallest solution with c = A366862(4) = 16.
%e a(5) = 12 is in the sequence since (a, b, c) = (73, 24, 12) is the smallest solution with c = A366862(5) = 12.
%o (PARI) S=[]; for(a=1,oo, for(b=2,a-1, for(c=1,b-1, issquare(a*b+c)&& issquare(a*c+b)&& issquare(b*c+a)&& (S=setunion(S,[c])) &&print1(a", "))))
%Y Cf. A366862, A366861 (possible a-values listed in increasing order).
%K nonn
%O 1,1
%A _M. F. Hasler_, Oct 25 2023