A199891 Number of compositions of n such that the number of parts and the largest part and the smallest part are pairwise not coprime.

0, 0, 0, 1, 0, 2, 0, 4, 1, 8, 12, 31, 30, 50, 84, 166, 240, 367, 560, 970, 1647, 2736, 4340, 6924, 11185, 18334, 29875, 48272, 77632, 125262, 202838, 329098, 533758, 865248, 1402099, 2271831, 3680202, 5960113, 9650231, 15624475, 25301422, 40983324, 66398800

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

Cf. A200476.

Sequence in context: A305371 A355018 A177256 * A339417 A351558 A226240

Adjacent sequences: A199888 A199889 A199890 * A199892 A199893 A199894

Keyword

nonn

Author

Alois P. Heinz, Nov 11 2011

Status

approved