OFFSET
1,6
COMMENTS
The smallest example without an overall common divisor is [10,10,10,10,10,15] (and its permutations), for n = 65. - Franklin T. Adams-Watters, Nov 16 2011
The smallest example where all 3 common divisors are different is [6,6,6,12] (and its permutations), for n = 30. - Alois P. Heinz, Nov 16 2011
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..250
EXAMPLE
a(9) = 1: [3,3,3].
a(10) = 8: [2,2,2,4], [2,2,4,2], [2,4,2,2], [2,8], [4,2,2,2], [4,6], [6,4], [8,2].
MAPLE
b:= proc(n, t, g, k) option remember;
`if`(n=0, `if`(igcd(g, t)<>1 and igcd(k, t)<>1
and igcd(g, k)<>1, 1, 0),
add(b(n-i, t+1, max(i, g), min(i, k)), i=2..n))
end:
a:= n-> b(n, 0, 0, infinity):
seq(a(n), n=1..50);
MATHEMATICA
b[n_, t_, g_, k_] := b[n, t, g, k] = If[n == 0, If[GCD[g, t] != 1 && GCD[k, t] != 1 && GCD[g, k] != 1, 1, 0], Sum[b[n-i, t+1, Max[i, g], Min[i, k]], {i, 2, n}]]; a[n_] := b[n, 0, 0, Infinity]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Nov 06 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 11 2011
STATUS
approved