A213918 - OEIS

%I #31 Aug 02 2019 03:43:36

%S 1,1,2,6,36,210,14976,552720,309582000

%N 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 Examples of sets for the first few cases:

%e {1},

%e {1,2},

%e {2, 3, 4},

%e {6, 8, 9, 12},

%e {36, 40, 42, 45, 48},

%e {210, 216, 220, 224, 225, 240},

%e {14976, 14980, 14994, 15000, 15008, 15015, 15120},

%e {552720, 552825, 552960, 553000, 553014, 553140, 553280, 554400},

%e {309582000, 309583680, 309583800, 309583872, 309583890, 309584000, 309584025, 309584100, 309584160}.

%t ok[v_, n_] := v == Select[v, GCD[#, n] == Abs[n - #] &];

%t ric[p_, cc_, k_] :=

%t If[Length@p == k, sol = p; True,

%t   Block[{c = cc, x, r = False},

%t    While[c != {}, x = First@c; c = Rest@c;

%t     If[p == Select[p, GCD[#, x] == Abs[x - #] &] &&

%t      ric[Append[p, x], c, k], r = True; Break[]]]; r]];

%t a[k_] := Block[{n = 1, d}, While[Length[d = Divisors@n] < k - 1 ||

%t !ric[{n}, n + d, k], n++]; n];

%t Do[Print[n, " ", a[n], " ", sol], {n, 7}]

%Y Cf. A061799, A214799.

%K nonn,more

%O 1,3

%A _Phil Scovis_, Mar 04 2013

%E Corrected (with Mathematica program) by _Giovanni Resta_, Mar 05 2013. Entry revised by _N. J. A. Sloane_, Mar 05 2013

%E a(8) from _Robert Gerbicz_, Mar 05 2013

%E a(9) from _Robert Gerbicz_, Mar 06 2013