A275307 -id:A275307 - cp's OEIS frontend

A048143 Number of labeled connected simplicial complexes with n nodes.

1, 1, 1, 5, 84, 6348, 7743728, 2414572893530, 56130437190053299918162

Offset: 0

Greg Huber, May 12 1983

Also number of connected antichains on a labeled n-set.

			For n=3 we could have 2 edges (in 3 ways), 3 edges (1 way), or 3 edges and a triangle (1 way), so a(3)=5.
a(5) = 1+75+645+1655+2005+1345+485+115+20+2 = 6348.

Patrick De Causmaecker, Stefan De Wannemacker, On the number of antichains of sets in a finite universe, arXiv:1407.4288 [math.CO], 2014.
Greg Huber, Letters to N. J. A. Sloane, May 1983 [Annotated, corrected, scanned copy]
Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.
Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Cf. A094033, A094034, A094035, A094036, A094037.

Cf. A000666, A006126, A030019, A054921, A120338, A275307, A285572.

More terms from Vladeta Jovovic, Jun 17 2006

Entry revised by N. J. A. Sloane, Jul 27 2006

A303362 Number of strict integer partitions of n with pairwise indivisible parts.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 3, 2, 3, 4, 5, 4, 6, 7, 7, 9, 11, 12, 13, 15, 17, 20, 23, 25, 27, 32, 35, 40, 45, 50, 55, 58, 67, 78, 84, 95, 101, 113, 124, 137, 153, 169, 180, 198, 219, 242, 268, 291, 319, 342, 374, 412, 450, 492, 535, 573, 632, 685, 746, 813, 868, 944

Offset: 1

Gus Wiseman, Apr 22 2018

nonn

			The a(14) = 7 strict integer partitions are (14), (11,3), (10,4), (9,5), (8,6), (7,5,2), (7,4,3).

Fausto A. C. Cariboni, Table of n, a(n) for n = 1..450, (terms up to a(250) from Andrew Howroyd)

Cf. A000009, A000837, A003238, A006126, A051424, A259936, A275307, A281116, A285572, A285573, A290103, A293606, A293993, A303364.

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]==={}&]],{n,60}]

lista(nn)={local(Cache=Map());
  my(excl=vector(nn, n, sumdiv(n, d, 2^(n-d))));
  my(a(n, m=n, b=0)=
     if(n==0, 1,
        while(m>n || bittest(b,0), m--; b>>=1);
        my(hk=[n, m, b], z);
        if(!mapisdefined(Cache, hk, &z),
          z = if(m, self()(n, m-1, b>>1) + self()(n-m, m, bitor(b, excl[m])), 0);
          mapput(Cache, hk, z)); z));
   for(n=1, nn, print1(a(n), ", "))
} \\ Andrew Howroyd, Nov 02 2019

A303837 Number of z-trees with least common multiple n > 1.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 1, 3, 1, 4, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 10, 1, 1, 2, 1, 1, 4, 1, 2, 1, 4, 1, 6, 1, 1, 2, 2, 1, 4, 1, 4, 1, 1, 1, 10, 1, 1, 1

Offset: 1

Gus Wiseman, May 19 2018

nonn

Given a finite set S of positive integers greater than 1, let G(S) be the simple labeled graph with vertex set S and edges between any two vertices that have a common divisor greater than 1. For example, G({6,14,15,35}) is a 4-cycle. A set S is said to be connected if G(S) is a connected graph. The clutter density of S is defined to be Sum_{s in S} (omega(s) - 1) - omega(LCM(S)), where omega = A001221 and LCM is least common multiple. Then a z-tree is a finite connected set of pairwise indivisible positive integers greater than 1 with clutter density -1.
This is a generalization to multiset systems of the usual definition of hypertree (viz. connected hypergraph F such that two distinct hyperedges of F intersect in at most a common vertex and such that every cycle of F is contained in a hyperedge).
If n is squarefree with k prime factors, then a(n) = A030019(k).

			The a(72) = 6 z-trees together with the corresponding multiset systems (see A112798, A302242) are the following.
      (72): {{1,1,1,2,2}}
    (8,18): {{1,1,1},{1,2,2}}
    (8,36): {{1,1,1},{1,1,2,2}}
    (9,24): {{2,2},{1,1,1,2}}
   (6,8,9): {{1,2},{1,1,1},{2,2}}
  (8,9,12): {{1,1,1},{2,2},{1,1,2}}
The a(60) = 10 z-trees together with the corresponding multiset systems are the following.
       (60): {{1,1,2,3}}
     (4,30): {{1,1},{1,2,3}}
     (6,20): {{1,2},{1,1,3}}
    (10,12): {{1,3},{1,1,2}}
    (12,15): {{1,1,2},{2,3}}
    (12,20): {{1,1,2},{1,1,3}}
    (15,20): {{2,3},{1,1,3}}
   (4,6,10): {{1,1},{1,2},{1,3}}
   (4,6,15): {{1,1},{1,2},{2,3}}
  (4,10,15): {{1,1},{1,3},{2,3}}

Roland Bacher, On the enumeration of labelled hypertrees and of labelled bipartite trees, arXiv:1102.2708 [math.CO], 2011.

Cf. A006126, A030019, A048143, A076078, A112798, A275307, A285572, A286518, A286520, A293993, A293994, A302242, A303838, A304118.

zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c=={},s,zsm[Union[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
zensity[s_]:=Total[(PrimeNu[#]-1&)/@s]-PrimeNu[LCM@@s];
Table[Length[Select[Rest[Subsets[Rest[Divisors[n]]]],And[zensity[#]==-1,zsm[#]=={n},Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]=={}]&]],{n,2,50}]

A304118 Number of z-blobs with least common multiple n > 1.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1

Offset: 1

Gus Wiseman, May 19 2018

nonn

Given a finite set S of positive integers greater than 1, let G(S) be the simple labeled graph with vertex set S and edges between any two vertices that have a common divisor greater than 1. For example, G({6,14,15,35}) is a 4-cycle. A set S is said to be connected if G(S) is a connected graph. The clutter density of S is defined to be Sum_{s in S} (omega(s) - 1) - omega(LCM(S)), where omega = A001221 and LCM is least common multiple. A z-blob is a finite connected set S of pairwise indivisible positive integers greater than 1 such that no cap of S with at least two edges has clutter density -1.

If n is squarefree with k prime factors, then a(n) = A275307(k).

			The a(60) = 7 z-blobs together with the corresponding multiset systems (see A112798, A302242) are the following.
        (60): {{1,1,2,3}}
     (12,30): {{1,1,2},{1,2,3}}
     (20,30): {{1,1,3},{1,2,3}}
   (6,15,20): {{1,2},{2,3},{1,1,3}}
  (10,12,15): {{1,3},{1,1,2},{2,3}}
  (12,15,20): {{1,1,2},{2,3},{1,1,3}}
  (12,20,30): {{1,1,2},{1,1,3},{1,2,3}}
The a(120) = 14 z-blobs together with the corresponding multiset systems are the following.
       (120): {{1,1,1,2,3}}
     (24,30): {{1,1,1,2},{1,2,3}}
     (24,60): {{1,1,1,2},{1,1,2,3}}
     (30,40): {{1,2,3},{1,1,1,3}}
     (40,60): {{1,1,1,3},{1,1,2,3}}
   (6,15,40): {{1,2},{2,3},{1,1,1,3}}
  (10,15,24): {{1,3},{2,3},{1,1,1,2}}
  (12,15,40): {{1,1,2},{2,3},{1,1,1,3}}
  (12,30,40): {{1,1,2},{1,2,3},{1,1,1,3}}
  (15,20,24): {{2,3},{1,1,3},{1,1,1,2}}
  (15,24,40): {{2,3},{1,1,1,2},{1,1,1,3}}
  (20,24,30): {{1,1,3},{1,1,1,2},{1,2,3}}
  (24,30,40): {{1,1,1,2},{1,2,3},{1,1,1,3}}
  (24,40,60): {{1,1,1,2},{1,1,1,3},{1,1,2,3}}

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Cf. A006126, A030019, A048143, A076078, A112798, A134954, A275307, A285572, A286518, A286520, A293993, A293994, A302242, A303837, A303838.

zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c=={},s,zsm[Union[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
zensity[s_]:=Total[(PrimeNu[#]-1&)/@s]-PrimeNu[LCM@@s];
zreeQ[s_]:=And[Length[s]>=2,zensity[s]==-1];
zlobQ[s_]:=Apply[And,Composition[Not,zreeQ]/@Apply[LCM,zptns[s],{2}]];
zswell[s_]:=Union[LCM@@@Select[Subsets[s],Length[zsm[#]]==1&]];
zkernels[s_]:=Table[Select[s,Divisible[w,#]&],{w,zswell[s]}];
zptns[s_]:=Select[stableSets[zkernels[s],Length[Intersection[#1,#2]]>0&],Union@@#==s&];
stableSets[u_,Q_]:=If[Length[u]==0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r==w||Q[r,w]||Q[w,r]],Q]]]];
Table[If[n==1,0,Length[Select[Rest[Subsets[Rest[Divisors[n]]]],And[zsm[#]=={n},Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&]=={},zlobQ[#]]&]]],{n,100}]

A293510 Number of connected minimal covers of n vertices.

Original entry on oeis.org

1, 1, 1, 4, 23, 241, 3732, 83987, 2666729, 117807298, 7217946453, 612089089261, 71991021616582, 11761139981560581, 2675674695560997301, 849270038176762472316, 376910699272413914514283, 234289022942841270608166061, 204344856617470777364053906796

Offset: 0

Gus Wiseman, Oct 11 2017

nonn

A cover of a finite set S is a finite set of finite nonempty sets with union S. A cover is minimal if removing any edge results in a cover of strictly fewer vertices. A cover is connected if it is connected as a hypergraph or clutter. Note that minimality is with respect to covering rather than to connectedness (cf. A030019).

			The a(3) = 4 covers are: ((12)(13)), ((12)(23)), ((13)(23)), ((123)).

Cf. A030019, A046165, A048143, A275307, A283877.

nn=30;ser=Sum[(1+Sum[Binomial[n,i]*StirlingS2[i,k]*(2^k-k-1)^(n-i),{k,2,n},{i,k,n}])*x^n/n!,{n,0,nn}];
Table[n!*SeriesCoefficient[1+Log[ser],{x,0,n}],{n,0,nn}]

A304887 Number of non-isomorphic blobs of weight n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 3, 3, 8, 14

Offset: 0

Gus Wiseman, May 20 2018

A blob is a connected antichain of finite sets that cannot be capped by a hypertree with more than one branch. The weight of a blob is the sum of cardinalities of its elements. Weight is generally not the same as number of vertices (see A275307).

			Non-isomorphic representatives of the a(8) = 8 blobs are the following:
  {{1,2,3,4,5,6,7,8}}
  {{1,5,6},{2,3,4,5,6}}
  {{1,2,5,6},{3,4,5,6}}
  {{1,3,4,5},{2,3,4,5}}
  {{1,2},{1,3,4},{2,3,4}}
  {{1,4},{1,5},{2,3,4,5}}
  {{2,4},{1,2,5},{3,4,5}}
  {{1,2},{1,3},{2,4},{3,4}}

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Cf. A030019, A035053, A048143, A275307, A283877, A286520, A293607, A293993, A293994, A304118, A304867.

A303838 Number of z-forests with least common multiple n > 1.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 8, 1, 1, 2, 2, 2, 5, 1, 2, 2, 4, 1, 8, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 16, 1, 2, 3, 1, 2, 8, 1, 3, 2, 8, 1, 7, 1, 2, 3, 3, 2, 8, 1, 5, 1, 2, 1, 16, 2, 2

Offset: 1

Gus Wiseman, May 19 2018

nonn

Given a finite set S of positive integers greater than 1, let G(S) be the simple labeled graph with vertex set S and edges between any two vertices that have a common divisor greater than 1. For example, G({6,14,15,35}) is a 4-cycle. A set S is said to be connected if G(S) is a connected graph. The clutter density of S is defined to be Sum_{s in S} (omega(s) - 1) - omega(LCM(S)), where omega = A001221 and LCM is least common multiple. A z-forest is a finite set of pairwise indivisible positive integers greater than 1 such that all connected components are z-trees, meaning they have clutter density -1.
This is a generalization to multiset systems of the usual definition of hyperforest (viz. hypergraph F such that two distinct hyperedges of F intersect in at most a common vertex and such that every cycle of F is contained in a hyperedge).
If n is squarefree with k prime factors, then a(n) = A134954(k).
Differs from A324837 at positions {1, 180, 210, ...}. For example, a(210) = 55, A324837(210) = 49.

			The a(60) = 16 z-forests together with the corresponding multiset systems (see A112798, A302242) are the following.
       (60): {{1,1,2,3}}
     (3,20): {{2},{1,1,3}}
     (4,15): {{1,1},{2,3}}
     (4,30): {{1,1},{1,2,3}}
     (5,12): {{3},{1,1,2}}
     (6,20): {{1,2},{1,1,3}}
    (10,12): {{1,3},{1,1,2}}
    (12,15): {{1,1,2},{2,3}}
    (12,20): {{1,1,2},{1,1,3}}
    (15,20): {{2,3},{1,1,3}}
    (3,4,5): {{2},{1,1},{3}}
   (3,4,10): {{2},{1,1},{1,3}}
    (4,5,6): {{1,1},{3},{1,2}}
   (4,6,10): {{1,1},{1,2},{1,3}}
   (4,6,15): {{1,1},{1,2},{2,3}}
  (4,10,15): {{1,1},{1,3},{2,3}}

Gus Wiseman, Table of n, a(n) for n = 1..250
Roland Bacher, On the enumeration of labelled hypertrees and of labelled bipartite trees, arXiv:1102.2708 [math.CO], 2011.

Cf. A006126, A030019, A048143, A076078, A112798, A134954, A275307, A285572, A286518, A286520, A293993, A293994, A302242, A303837, A304118.

zsm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[Less@@#,GCD@@s[[#]]]>1&]},If[c=={},s,zsm[Union[Append[Delete[s,List/@c[[1]]],LCM@@s[[c[[1]]]]]]]]];
zensity[s_]:=Total[(PrimeNu[#]-1&)/@s]-PrimeNu[LCM@@s];
Table[Length[Select[Rest[Subsets[Rest[Divisors[n]]]],Function[s,LCM@@s==n&&And@@Table[zensity[Select[s,Divisible[m,#]&]]==-1,{m,zsm[s]}]&&Select[Tuples[s,2],UnsameQ@@#&&Divisible@@#&]=={}]]],{n,100}]

A317672 Regular triangle where T(n,k) is the number of clutters (connected antichains) on n + 1 vertices with k maximal blobs (2-connected components).

Original entry on oeis.org

1, 2, 3, 44, 24, 16, 4983, 940, 300, 125, 7565342, 154770, 18000, 4320, 1296, 2414249587694, 318926314, 3927105, 363580, 72030, 16807, 56130437054842366160898, 135200580256336, 10244647168, 99187200, 8028160, 1376256, 262144

Offset: 1

Gus Wiseman, Aug 03 2018

			Triangle begins:
        1
        2       3
       44      24      16
     4983     940     300     125
  7565342  154770   18000    4320    1296

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Row sums are A048143. First column is A275307. Last column is A030019.

Cf. A000272, A001187, A002218, A013922, A134954, A293510, A317631, A317632, A317634, A317635, A317671.

blg={0,1,2,44,4983,7565342,2414249587694,56130437054842366160898} (* A275307 *);
sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Sum[n^(k-1)*Product[blg[[Length[s]+1]],{s,spn}],{spn,Select[sps[Range[n-1]],Length[#]==k&]}],{n,Length[blg]},{k,n-1}]

A326751 BII-numbers of blobs.

Original entry on oeis.org

0, 1, 2, 4, 8, 16, 32, 52, 64, 128, 256, 512, 772, 816, 820, 832, 1024, 1072, 1088, 2048, 2320, 2340, 2356, 2368, 2580, 2592, 2612, 2624, 2836, 2852, 2864, 2868, 2880, 3088, 3104, 3120, 3136, 4096, 4132, 4160, 4612, 4640, 4644, 4672, 5120, 5152, 5184, 8192

Offset: 1

Gus Wiseman, Jul 23 2019

nonn

A binary index of n is any position of a 1 in its reversed binary expansion. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every finite set of finite nonempty sets has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18.

Elements of a set-system are sometimes called edges. In an antichain, no edge is a subset or superset of any other edge. In a 2-vertex-connected set-system, at least two vertices must be removed to make the set-system disconnected. A blob is a connected, 2-vertex-connected antichain of finite, nonempty sets, or, equivalently, a 2-vertex-connected clutter.

			The sequence of all blobs together with their BII-numbers begins:
     0: {}
     1: {{1}}
     2: {{2}}
     4: {{1,2}}
     8: {{3}}
    16: {{1,3}}
    32: {{2,3}}
    52: {{1,2},{1,3},{2,3}}
    64: {{1,2,3}}
   128: {{4}}
   256: {{1,4}}
   512: {{2,4}}
   772: {{1,2},{1,4},{2,4}}
   816: {{1,3},{2,3},{1,4},{2,4}}
   820: {{1,2},{1,3},{2,3},{1,4},{2,4}}
   832: {{1,2,3},{1,4},{2,4}}
  1024: {{1,2,4}}
  1072: {{1,3},{2,3},{1,2,4}}
  1088: {{1,2,3},{1,2,4}}
  2048: {{3,4}}
  2320: {{1,3},{1,4},{3,4}}
  2340: {{1,2},{2,3},{1,4},{3,4}}
  2356: {{1,2},{1,3},{2,3},{1,4},{3,4}}

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Cf. A000120, A002218, A013922 (2-vertex-connected graphs), A030019, A048143 (clutters), A048793, A070939, A095983, A275307 (spanning blobs), A304118, A304887, A322117, A322397 (2-edge-connected clutters), A326031.

Other BII-numbers: A309314 (hyperforests), A326701 (set partitions), A326703 (chains), A326704 (antichains), A326749 (connected), A326750 (clutters), A326752 (hypertrees), A326754 (covers).

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
tvcQ[eds_]:=And@@Table[Length[csm[DeleteCases[eds,i,{2}]]]<=1,{i,Union@@eds}];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
Select[Range[0,1000],stableQ[bpe/@bpe[#],SubsetQ]&&Length[csm[bpe/@bpe[#]]]<=1&&tvcQ[bpe/@bpe[#]]&]

A322335 Number of 2-edge-connected integer partitions of n.

Original entry on oeis.org

0, 0, 0, 1, 0, 3, 0, 4, 2, 7, 0, 13, 0, 15, 8, 21, 1, 37, 2, 45, 18, 58, 8, 95, 19, 109, 45, 150, 38, 232, 59, 268, 129, 357, 155, 523, 203, 633, 359, 852, 431, 1185, 609, 1464, 969

Offset: 1

Gus Wiseman, Dec 04 2018

First differs from A108572 at a(17) = 1, A108572(17) = 0.

An integer partition is 2-edge-connected if the hypergraph of prime factorizations of its parts is connected and cannot be disconnected by removing any single part. For example (6,6,3,2) is 2-edge-connected but (6,3,2) is not.

			The a(14) = 15 2-edge-connected integer partitions of 14:
  (7,7)   (6,4,4)   (4,4,4,2)  (4,4,2,2,2)  (4,2,2,2,2,2)  (2,2,2,2,2,2,2)
  (8,6)   (6,6,2)   (6,4,2,2)  (6,2,2,2,2)
  (10,4)  (8,4,2)   (8,2,2,2)
  (12,2)  (10,2,2)

Wikipedia, k-edge-connected graph

Cf. A007718, A013922, A054921, A095983, A218970, A275307, A286518, A304714, A304716, A322336, A322337, A322338.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
twoedQ[sys_]:=And[Length[csm[sys]]==1,And@@Table[Length[csm[Delete[sys,i]]]==1,{i,Length[sys]}]];
Table[Length[Select[IntegerPartitions[n],twoedQ[primeMS/@#]&]],{n,30}]

a(42)-a(45) from Jinyuan Wang, Jun 20 2020

cp's OEIS Frontend

A048143 Number of labeled connected simplicial complexes with n nodes.

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A303362 Number of strict integer partitions of n with pairwise indivisible parts.

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PARI

A303837 Number of z-trees with least common multiple n > 1.

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A304118 Number of z-blobs with least common multiple n > 1.

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A293510 Number of connected minimal covers of n vertices.

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A304887 Number of non-isomorphic blobs of weight n.

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A303838 Number of z-forests with least common multiple n > 1.

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A317672 Regular triangle where T(n,k) is the number of clutters (connected antichains) on n + 1 vertices with k maximal blobs (2-connected components).

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A326751 BII-numbers of blobs.

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