The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000741 Number of compositions of n into 3 ordered relatively prime parts. (Formerly M2531 N0999) 19
 0, 0, 1, 3, 6, 9, 15, 18, 27, 30, 45, 42, 66, 63, 84, 84, 120, 99, 153, 132, 174, 165, 231, 180, 270, 234, 297, 270, 378, 276, 435, 360, 450, 408, 540, 414, 630, 513, 636, 552, 780, 558, 861, 690, 828, 759, 1035, 744, 1113, 870, 1104, 972, 1326, 945, 1380, 1116, 1386, 1218 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2(4) (1964), 241-260. C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003. N. J. A. Sloane, Transforms FORMULA Moebius transform of A000217(n-2). 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 EXAMPLE From Gus Wiseman, Oct 14 2020: (Start) The a(3) = 1 through a(8) = 18 triples:   (1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)            (1,2,1)  (1,2,2)  (1,2,3)  (1,2,4)  (1,2,5)            (2,1,1)  (1,3,1)  (1,3,2)  (1,3,3)  (1,3,4)                     (2,1,2)  (1,4,1)  (1,4,2)  (1,4,3)                     (2,2,1)  (2,1,3)  (1,5,1)  (1,5,2)                     (3,1,1)  (2,3,1)  (2,1,4)  (1,6,1)                              (3,1,2)  (2,2,3)  (2,1,5)                              (3,2,1)  (2,3,2)  (2,3,3)                              (4,1,1)  (2,4,1)  (2,5,1)                                       (3,1,3)  (3,1,4)                                       (3,2,2)  (3,2,3)                                       (3,3,1)  (3,3,2)                                       (4,1,2)  (3,4,1)                                       (4,2,1)  (4,1,3)                                       (5,1,1)  (4,3,1)                                                (5,1,2)                                                (5,2,1)                                                (6,1,1) (End) MAPLE with(numtheory): mobtr:= proc(p)           proc(n) option remember;             add(mobius(n/d)*p(d), d=divisors(n))           end         end: A000217:= n-> n*(n+1)/2: a:= mobtr(n-> A000217(n-2)): seq(a(n), n=1..58);  # Alois P. Heinz, Feb 08 2011 MATHEMATICA 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-François Alcover, Mar 12 2014, after Alois P. Heinz *) Table[Length[Select[Join@@Permutations/@IntegerPartitions[n, {3}], GCD@@#==1&]], {n, 0, 30}] (* Gus Wiseman, Oct 14 2020 *) CROSSREFS A000010 is the length-2 version. A000217(n-2) does not require relative primality. A000740 counts these compositions of any length. A000742 is the length-4 version. A000837 counts relatively prime partitions. A023023 is the unordered version. A101271 is the strict case. A101391 has this as column k = 3. A284825*6 is the pairwise non-coprime case. A291166 intersected with A014311 ranks these compositions. A337461 is the pairwise coprime instead of relatively prime version. A337603 counts length-3 compositions whose distinct parts are pairwise coprime. A337604 is the pairwise non-coprime instead of relatively prime version. Cf. A001399, A007997, A023022, A078374, A337450, A337451, A337602. Sequence in context: A133331 A276381 A259728 * A133205 A049991 A143981 Adjacent sequences:  A000738 A000739 A000740 * A000742 A000743 A000744 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by Alois P. Heinz, Feb 08 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 4 11:02 EDT 2022. Contains 355075 sequences. (Running on oeis4.)