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A213918 a(n) = smallest possible element of a set of n positive integers s_1, s_2, ..., s_n such that for i != j, |s_i - s_j| = gcd(s_i, s_j), where |x| denotes absolute value.

%I A213918 #31 Aug 02 2019 03:43:36
%S A213918 1,1,2,6,36,210,14976,552720,309582000
%N A213918 a(n) = smallest possible element of a set of n positive integers s_1, s_2, ..., s_n such that for i != j,  |s_i - s_j| = gcd(s_i, s_j), where |x| denotes absolute value.
%e A213918 Examples of sets for the first few cases:
%e A213918 {1},
%e A213918 {1,2},
%e A213918 {2, 3, 4},
%e A213918 {6, 8, 9, 12},
%e A213918 {36, 40, 42, 45, 48},
%e A213918 {210, 216, 220, 224, 225, 240},
%e A213918 {14976, 14980, 14994, 15000, 15008, 15015, 15120},
%e A213918 {552720, 552825, 552960, 553000, 553014, 553140, 553280, 554400},
%e A213918 {309582000, 309583680, 309583800, 309583872, 309583890, 309584000, 309584025, 309584100, 309584160}.
%t A213918 ok[v_, n_] := v == Select[v, GCD[#, n] == Abs[n - #] &];
%t A213918 ric[p_, cc_, k_] :=
%t A213918 If[Length@p == k, sol = p; True,
%t A213918   Block[{c = cc, x, r = False},
%t A213918    While[c != {}, x = First@c; c = Rest@c;
%t A213918     If[p == Select[p, GCD[#, x] == Abs[x - #] &] &&
%t A213918      ric[Append[p, x], c, k], r = True; Break[]]]; r]];
%t A213918 a[k_] := Block[{n = 1, d}, While[Length[d = Divisors@n] < k - 1 ||
%t A213918 !ric[{n}, n + d, k], n++]; n];
%t A213918 Do[Print[n, " ", a[n], " ", sol], {n, 7}]
%Y A213918 Cf. A061799, A214799.
%K A213918 nonn,more
%O A213918 1,3
%A A213918 _Phil Scovis_, Mar 04 2013
%E A213918 Corrected (with Mathematica program) by _Giovanni Resta_, Mar 05 2013. Entry revised by _N. J. A. Sloane_, Mar 05 2013
%E A213918 a(8) from _Robert Gerbicz_, Mar 05 2013
%E A213918 a(9) from _Robert Gerbicz_, Mar 06 2013