cp's OEIS Frontend

A337601 Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is not considered coprime unless it is (1).

%I A337601 #13 Jan 18 2021 02:41:33
%S A337601 0,0,0,1,1,2,2,3,4,4,5,6,8,7,10,7,11,11,17,12,19,12,19,17,29,16,28,19,
%T A337601 31,23,46,23,42,25,45,27,59,31,57,34,61,37,84,38,75,42,74,47,107,45,
%U A337601 98,51,96,56,135,54,115,63,117,67,174,65,139,75,144,75,194
%N A337601 Number of unordered triples of positive integers summing to n whose set of distinct parts is pairwise coprime, where a singleton is not considered coprime unless it is (1).
%C A337601 First differs from A337600 at a(9) = 4, A337600(9) = 5.
%H A337601 Fausto A. C. Cariboni, <a href="/A337601/b337601.txt">Table of n, a(n) for n = 0..10000</a>
%F A337601 For n > 0, a(n) = A337600(n) - A079978(n).
%e A337601 The a(3) = 1 through a(14) = 10 partitions (A = 10, B = 11, C = 12):
%e A337601   111  211  221  321  322  332  441  433  443  543  544  554
%e A337601             311  411  331  431  522  532  533  552  553  743
%e A337601                       511  521  531  541  551  651  661  752
%e A337601                            611  711  721  722  732  733  761
%e A337601                                      811  731  741  751  833
%e A337601                                           911  831  922  851
%e A337601                                                921  B11  941
%e A337601                                                A11       A31
%e A337601                                                          B21
%e A337601                                                          C11
%t A337601 Table[Length[Select[IntegerPartitions[n,{3}],CoprimeQ@@Union[#]&]],{n,0,100}]
%Y A337601 A014612 intersected with A304711 ranks these partitions.
%Y A337601 A220377 is the strict case.
%Y A337601 A304709 counts these partitions of any length.
%Y A337601 A307719 is the strict case except for any number of 1's.
%Y A337601 A337600 considers singletons to be coprime.
%Y A337601 A337603 is the ordered version.
%Y A337601 A000217 counts 3-part compositions.
%Y A337601 A000837 counts relatively prime partitions.
%Y A337601 A001399/A069905/A211540 count 3-part partitions.
%Y A337601 A023023 counts relatively prime 3-part partitions.
%Y A337601 A051424 counts pairwise coprime or singleton partitions.
%Y A337601 A101268 counts pairwise coprime or singleton compositions.
%Y A337601 A305713 counts pairwise coprime strict partitions.
%Y A337601 A327516 counts pairwise coprime partitions.
%Y A337601 A333227 ranks pairwise coprime compositions.
%Y A337601 A333228 ranks compositions whose distinct parts are pairwise coprime.
%Y A337601 A337461 counts pairwise coprime 3-part compositions.
%Y A337601 Cf. A001840, A007359, A007360, A087087, A284825, A302696, A304712, A328673, A335238, A337602.
%K A337601 nonn
%O A337601 0,6
%A A337601 _Gus Wiseman_, Sep 20 2020