cp's OEIS Frontend

A337600 Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.

%I A337600 #15 Jan 18 2021 02:41:26
%S A337600 0,0,0,1,1,2,3,3,4,5,5,6,9,7,10,8,11,11,18,12,19,13,19,17,30,16,28,20,
%T A337600 31,23,47,23,42,26,45,27,60,31,57,35,61,37,85,38,75,43,74,47,108,45,
%U A337600 98,52,96,56,136,54,115,64,117,67,175,65,139,76,144,75,195
%N A337600 Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is always considered coprime.
%C A337600 First differs from A337601 at a(9) = 5, A337601(9) = 4.
%H A337600 Fausto A. C. Cariboni, <a href="/A337600/b337600.txt">Table of n, a(n) for n = 0..10000</a>
%F A337600 For n > 0, a(n) = A337601(n) + A079978(n).
%e A337600 The a(3) = 1 through a(14) = 10 partitions (A = 10, B = 11, C = 12):
%e A337600   111  211  221  222  322  332  333  433  443  444  544  554
%e A337600             311  321  331  431  441  532  533  543  553  743
%e A337600                  411  511  521  522  541  551  552  661  752
%e A337600                            611  531  721  722  651  733  761
%e A337600                                 711  811  731  732  751  833
%e A337600                                           911  741  922  851
%e A337600                                                831  B11  941
%e A337600                                                921       A31
%e A337600                                                A11       B21
%e A337600                                                          C11
%t A337600 Table[Length[Select[IntegerPartitions[n,{3}],SameQ@@#||CoprimeQ@@Union[#]&]],{n,0,100}]
%Y A337600 A220377 is the strict case.
%Y A337600 A304712 counts these partitions of any length.
%Y A337600 A307719 is the strict case except for any number of 1's.
%Y A337600 A337601 does not consider a singleton to be coprime unless it is (1).
%Y A337600 A337602 is the ordered version.
%Y A337600 A337664 counts compositions of this type and any length.
%Y A337600 A000217 counts 3-part compositions.
%Y A337600 A000837 counts relatively prime partitions.
%Y A337600 A001399/A069905/A211540 count 3-part partitions.
%Y A337600 A023023 counts relatively prime 3-part partitions.
%Y A337600 A051424 counts pairwise coprime or singleton partitions.
%Y A337600 A101268 counts pairwise coprime or singleton compositions.
%Y A337600 A304709 counts partitions whose distinct parts are pairwise coprime.
%Y A337600 A305713 counts pairwise coprime strict partitions.
%Y A337600 A327516 counts pairwise coprime partitions.
%Y A337600 A333227 ranks pairwise coprime compositions.
%Y A337600 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337600 A337461 counts pairwise coprime length-3 compositions.
%Y A337600 A337563 counts pairwise coprime length-3 partitions with no 1's.
%Y A337600 Cf. A001840, A007359, A007360, A014612, A087087, A284825, A302569, A302696, A328673, A335235, A337603, A337695.
%K A337600 nonn
%O A337600 0,6
%A A337600 _Gus Wiseman_, Sep 20 2020