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%I #15 Nov 16 2014 15:54:03
%S 1,2,2,7,7,18,40,85,148,285,584,1231,2516,5069,10175,20306,40000,
%T 78328,154233,307586,620903,1262129,2566697,5193429,10424746,20761986,
%U 41131719,81358316,161239595,320900400,641688619,1287937462,2589941043,5208522925,10461756080
%N Number of compositions of n such that the number of parts and the greatest part are coprime.
%H Alois P. Heinz, <a href="/A199886/b199886.txt">Table of n, a(n) for n = 1..350</a>
%F a(n) = A000079(n-1) - A199887(n).
%e a(5) = 7: [1,1,1,1,1], [1,2,2], [2,1,2], [2,2,1], [2,3], [3,2], [5].
%p b:= proc(n, t, g) option remember;
%p `if`(n=0, `if`(igcd(g, t)=1, 1, 0),
%p add(b(n-i, t+1, max(i, g)), i=1..n))
%p end:
%p a:= n-> b(n, 0, 0):
%p seq(a(n), n=1..40);
%t 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_ *)
%Y Cf. A000079, A199887.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Nov 11 2011
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