|
%I #5 Mar 04 2018 23:17:37
%S 0,1,1,1,1,1,2,1,1,1,4,1,11,2,2,1,33,1,116,1,5,4,435,1,2,11,1,2,1832,
%T 2,8167,1,12,33,10,1,39700,116,37,1,201785,5,1099449,4,3,435,6237505,
%U 1,19,2,123,11,37406458,1,27,2,474,1832,232176847,2,1513796040
%N In the ranked poset of integer partitions ordered by refinement, number of maximal chains from the local minimum to the partition with Heinz number n.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e The a(21) = 5 maximal chains are the rows:
%e (111111)<(21111)<(2211)<(222)<(42)
%e (111111)<(21111)<(2211)<(411)<(42)
%e (111111)<(21111)<(2211)<(321)<(42)
%e (111111)<(21111)<(3111)<(411)<(42)
%e (111111)<(21111)<(3111)<(321)<(42)
%t pcovs[ptn_]:=Select[Union[Reverse/@Sort/@Join@@@Tuples[IntegerPartitions/@ptn]],Length[#]===Length[ptn]+1&];
%t coc[ptn_]:=coc[ptn]=If[Max[ptn]===1,1,Total[coc/@pcovs[ptn]]];
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[coc[Reverse[primeMS[n]]],{n,50}]
%Y Cf. A000041, A001055, A001222, A002846, A056239, A112798, A213427, A215366, A265947, A296150, A299200, A299202, A299925, A300273, A300383, A300385.
%K nonn
%O 1,7
%A _Gus Wiseman_, Mar 04 2018
|
