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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316655 Number of series-reduced rooted trees whose leaves span an initial interval of positive integers with multiplicities the integer partition with Heinz number n. 16

%I #9 Sep 14 2018 02:34:18

%S 0,1,1,1,2,3,5,4,12,9,12,17,33,29,44,26,90,90,261,68,168,93,766,144,

%T 197,307,575,269,2312,428,7068,236,625,1017,863,954,21965,3409,2342,

%U 712

%N Number of series-reduced rooted trees whose leaves span an initial interval of positive integers with multiplicities the integer partition with Heinz number n.

%C A rooted tree is series-reduced if every non-leaf node has at least two branches.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%F a(prime(n)) = A000669(n).

%F a(2^n) = A000311(n).

%e Sequence of sets of trees begins:

%e 1:

%e 2: 1

%e 3: (11)

%e 4: (12)

%e 5: (1(11)), (111)

%e 6: (1(12)), (2(11)), (112)

%e 7: (1(1(11))), (1(111)), ((11)(11)), (11(11)), (1111)

%e 8: (1(23)), (2(13)), (3(12)), (123)

%e 9: (1(1(22))), (1(2(12))), (1(122)), (2(1(12))), (2(2(11))), (2(112)), ((11)(22)), ((12)(12)), (11(22)), (12(12)), (22(11)), (1122)

%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];

%t mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];

%t gro[m_]:=If[Length[m]==1,m,Union[Sort/@Join@@(Tuples[gro/@#]&/@Select[mps[m],Length[#]>1&])]];

%t Table[Length[gro[Flatten[MapIndexed[Table[#2,{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]]]]],{n,20}]

%Y Cf. A000081, A000311, A000669, A001678, A005804, A056239, A141268, A181821, A292504, A296150, A300660, A304660.

%Y Cf. A316651, A316652, A316653, A316654, A316656.

%K nonn,more

%O 1,5

%A _Gus Wiseman_, Jul 09 2018

%E a(37)-a(40) from _Robert Price_, Sep 13 2018

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:43 EDT 2024. Contains 371264 sequences. (Running on oeis4.)