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A199887 Number of compositions of n such that the number of parts and the greatest part are not coprime. 3
0, 0, 2, 1, 9, 14, 24, 43, 108, 227, 440, 817, 1580, 3123, 6209, 12462, 25536, 52744, 107911, 216702, 427673, 835023, 1627607, 3195179, 6352470, 12792446, 25977145, 52859412, 107195861, 215970512, 432053205, 859546186, 1705026253, 3381411667, 6718113104 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = A000079(n-1) - A199886(n).
EXAMPLE
a(5) = 9: [1,1,1,2], [1,1,2,1], [1,1,3], [1,2,1,1], [1,3,1], [1,4], [2,1,1,1], [3,1,1], [4,1].
MAPLE
b:= proc(n, t, g) option remember;
`if`(n=0, `if`(igcd(g, t)<>1, 1, 0),
add(b(n-i, t+1, max(i, g)), i=1..n))
end:
a:= n-> b(n, 0, 0):
seq(a(n), n=1..40);
MATHEMATICA
b[n_, t_, g_] := b[n, t, g] = If[n == 0, If[GCD[g, t] != 1, 1, 0], Sum[b[n-i, t+1, Max[i, g]], {i, 1, n}]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Nov 05 2014, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A192352 A180001 A204371 * A058876 A214884 A083162
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 11 2011
STATUS
approved

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Last modified December 7 10:56 EST 2023. Contains 367650 sequences. (Running on oeis4.)