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A000741 Number of compositions of n into 3 ordered relatively prime parts.
(Formerly M2531 N0999)
13

%I M2531 N0999

%S 0,0,1,3,6,9,15,18,27,30,45,42,66,63,84,84,120,99,153,132,174,165,231,

%T 180,270,234,297,270,378,276,435,360,450,408,540,414,630,513,636,552,

%U 780,558,861,690,828,759,1035,744,1113,870,1104,972,1326,945,1380,1116,1386,1218

%N Number of compositions of n into 3 ordered relatively prime parts.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A000741/b000741.txt">Table of n, a(n) for n = 1..10000</a>

%H H. W. Gould, <a href="http://www.fq.math.ca/Scanned/2-4/gould.pdf">Binomial coefficients, the bracket function and compositions with relatively prime summands</a>, Fib. Quart. 2(4) (1964), 241-260.

%H C. Kimberling, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Kimberling/kimberling24.html">Matrix Transformations of Integer Sequences</a>, J. Integer Seqs., Vol. 6, 2003.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F Moebius transform of A000217(n-2).

%F G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = (1 - 3*x + 3*x^2)/(1 - x)^3. - _Ilya Gutkovskiy_, Apr 26 2017

%p with (numtheory):

%p mobtr:= proc(p)

%p proc(n) option remember;

%p add (mobius(n/d)*p(d), d=divisors(n))

%p end

%p end:

%p A000217:= n-> n*(n+1)/2:

%p a:= mobtr (n-> A000217(n-2)):

%p seq (a(n), n=1..58); # _Alois P. Heinz_, Feb 08 2011

%t mobtr[p_] := Module[{f}, f[n_] := f[n] = Sum[MoebiusMu[n/d]*p[d], {d, Divisors[n]}]; f]; A000217[n_] := n*(n+1)/2; a = mobtr[A000217[#-2]&]; Table[a[n], {n, 1, 58}] (* _Jean-Fran├žois Alcover_, Mar 12 2014, after _Alois P. Heinz_ *)

%K nonn,easy

%O 1,4

%A _N. J. A. Sloane_.

%E Edited by _Alois P. Heinz_, Feb 08 2011

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Last modified August 11 13:02 EDT 2020. Contains 336428 sequences. (Running on oeis4.)