cp's OEIS Frontend

A367587 Least element in row n of A367858 (multiset multiplicity cokernel).

%I A367587 #6 Dec 03 2023 23:30:56
%S A367587 0,1,2,1,3,2,4,1,2,3,5,1,6,4,3,1,7,1,8,1,4,5,9,1,3,6,2,1,10,3,11,1,5,
%T A367587 7,4,2,12,8,6,1,13,4,14,1,2,9,15,1,4,1,7,1,16,1,5,1,8,10,17,1,18,11,2,
%U A367587 1,6,5,19,1,9,4,20,1,21,12,2,1,5,6,22,1,2
%N A367587 Least element in row n of A367858 (multiset multiplicity cokernel).
%C A367587 We define the multiset multiplicity cokernel MMC(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then max(S) has multiplicity |S| in MMC(m). For example, MMC({1,1,2,2,3,4,5}) = {2,2,5,5,5}, and MMC({1,2,3,4,5,5,5,5}) = {4,4,4,4,5}. As an operation on multisets MMC is represented by A367858, and as an operation on their ranks it is represented by A367859.
%F A367587 a(n) = A055396(A367859(n)).
%F A367587 a(n^k) = a(n) for all positive integers n and k.
%F A367587 If n is a power of a squarefree number, a(n) = A061395(n).
%t A367587 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A367587 mmc[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Max@@Select[q,Count[q,#]==i&],{i,mts}]]];
%t A367587 Table[If[n==1,0,Min@@mmc[prix[n]]],{n,100}]
%Y A367587 Indices of first appearances are A008578.
%Y A367587 Depends only on rootless base A052410, see A007916.
%Y A367587 For kernel instead of cokernel we have A055396.
%Y A367587 For maximum instead of minimum element we have A061395.
%Y A367587 The opposite version is A367583.
%Y A367587 Row-minima of A367858.
%Y A367587 A007947 gives squarefree kernel.
%Y A367587 A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
%Y A367587 A124010 lists prime multiplicities (prime signature), sorted A118914.
%Y A367587 A181819 gives prime shadow, with an inverse A181821.
%Y A367587 A238747 gives prime metasignature, sorted A353742.
%Y A367587 A304038 lists distinct prime indices, length A001221, sum A066328.
%Y A367587 A367579 lists MMK, rank A367580, sum A367581, max A367583, min A055396.
%Y A367587 Cf. A000720, A027746, A051904, A071625, A072774, A130091, A367582, A367584, A367585, A367586.
%K A367587 nonn
%O A367587 1,3
%A A367587 _Gus Wiseman_, Dec 03 2023