

A199891


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


2



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
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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. AdamsWatters, 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



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(ni, 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[ni, t+1, Max[i, g], Min[i, k]], {i, 2, n}]]; a[n_] := b[n, 0, 0, Infinity]; Table[a[n], {n, 1, 50}] (* JeanFrançois Alcover, Nov 06 2014, after Alois P. Heinz *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



