cp's OEIS Frontend

A343659 Number of maximal pairwise coprime subsets of {1..n}.

%I A343659 #24 May 05 2021 02:11:23
%S A343659 1,1,1,2,2,3,3,4,7,9,9,10,10,12,16,19,19,20,20,22,28,32,32,33,54,61,
%T A343659 77,84,84,85,85,94,112,123,158,161,161,176,206,212,212,214,214,229,
%U A343659 241,260,260,263,417,428,490,521,521,526,655,674,764,818,818,820,820,874,918,975,1182,1189,1189
%N A343659 Number of maximal pairwise coprime subsets of {1..n}.
%C A343659 For this sequence, it does not matter whether singletons are considered pairwise coprime.
%C A343659 For n > 2, also the number of maximal pairwise coprime subsets of {2..n}.
%C A343659 For each prime p <= n, p divides exactly one element of each maximal subset. - _Bert Dobbelaere_, May 04 2021
%H A343659 Bert Dobbelaere, <a href="/A343659/b343659.txt">Table of n, a(n) for n = 1..500</a>
%H A343659 Bert Dobbelaere, <a href="/A343659/a343659.py.txt">Python program</a>
%e A343659 The a(1) = 1 through a(9) = 7 subsets:
%e A343659   {1}  {12}  {123}  {123}  {1235}  {156}   {1567}   {1567}   {1567}
%e A343659                     {134}  {1345}  {1235}  {12357}  {12357}  {12357}
%e A343659                                    {1345}  {13457}  {13457}  {12579}
%e A343659                                                     {13578}  {13457}
%e A343659                                                              {13578}
%e A343659                                                              {14579}
%e A343659                                                              {15789}
%t A343659 fasmax[y_]:=Complement[y,Union@@Most@*Subsets/@y];
%t A343659 Table[Length[fasmax[Select[Subsets[Range[n]],CoprimeQ@@#&]]],{n,15}]
%Y A343659 The case of pairs is A015614.
%Y A343659 The case of triples is A015617.
%Y A343659 The non-maximal version counting empty sets and singletons is A084422.
%Y A343659 The non-maximal version counting singletons is A187106.
%Y A343659 The non-maximal version is A320426(n) = A276187(n) + 1.
%Y A343659 The version for indivisibility instead of coprimality is A326077.
%Y A343659 The version for sets of divisors is A343652.
%Y A343659 The version for sets of divisors > 1 is A343660.
%Y A343659 A018892 counts coprime unordered pairs of divisors.
%Y A343659 A051026 counts pairwise indivisible subsets of {1..n}.
%Y A343659 A100565 counts pairwise coprime unordered triples of divisors.
%Y A343659 Cf. A007360, A067824, A087087, A225520, A324837, A325683, A325859, A326358, A326496, A326675, A333227, A343653, A343655.
%K A343659 nonn
%O A343659 1,4
%A A343659 _Gus Wiseman_, Apr 26 2021
%E A343659 More terms from _Bert Dobbelaere_, May 04 2021