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A280244 Lexicographically ordered list of sequences that meet the criteria for R. L. Graham's sequence: k = a_1 < a_2 < ... < a_t = A006255(k) and a_1*a_2*...*a_t is a square.

%I A280244 #20 Oct 28 2021 07:11:00
%S A280244 1,2,3,4,6,2,3,6,3,4,6,8,3,6,8,4,5,8,9,10,5,8,10,6,8,9,12,6,8,12,7,8,
%T A280244 9,14,7,8,14,8,9,10,12,15,8,10,12,15,9,10,12,15,16,18,10,12,15,18,11,
%U A280244 12,14,16,21,22,11,12,14,21,22,11,12,15,16,18,20,22
%N A280244 Lexicographically ordered list of sequences that meet the criteria for R. L. Graham's sequence: k = a_1 < a_2 < ... < a_t = A006255(k) and a_1*a_2*...*a_t is a square.
%C A280244 A259527(n) rows begin with n.
%H A280244 Peter Kagey, <a href="/A280244/b280244.txt">Table of n, a(n) for n = 1..10000</a>
%e A280244 [8,9,10,12,15] appears as a row in the table because A006255(8) = 15 and the product of the row is a square: 8*9*10*12*15 = 360^2.
%e A280244 Table begins:
%e A280244   1;
%e A280244   2,  3,  4,  6;
%e A280244   2,  3,  6;
%e A280244   3,  4,  6,  8;
%e A280244   3,  6,  8;
%e A280244   4;
%e A280244   5,  8,  9, 10;
%e A280244   5,  8, 10;
%e A280244   6,  8,  9, 12;
%e A280244   6,  8, 12;
%e A280244   7,  8,  9, 14;
%e A280244   7,  8, 14;
%e A280244   8,  9, 10, 12, 15;
%e A280244   8, 10, 12, 15;
%e A280244   ...
%t A280244 MapIndexed[With[{b = #1, a = First@ #2}, Reverse@ Select[Rest@ Subsets@ Range[a, b], And[SubsetQ[#, {a, b}], IntegerQ@ Sqrt[Times @@ #]] &]] &, #] &@ Table[k = 0; Which[IntegerQ@ Sqrt@ n, k, And[PrimeQ@ n, n > 3], k = n, True, While[Length@ Select[n Map[Times @@ # &, n + Rest@ Subsets@ Range@ k], IntegerQ@ Sqrt@# &] == 0, k++]]; k + n, {n, 16}] // Flatten (* _Michael De Vlieger_, Dec 30 2016 *)
%Y A280244 Cf. A006255, A245499, A259527.
%K A280244 nonn,tabf,look
%O A280244 1,2
%A A280244 _Peter Kagey_, Dec 29 2016