cp's OEIS Frontend

A363486 Low mode in the multiset of prime indices of n.

%I A363486 #16 Jul 05 2023 21:37:45
%S A363486 0,1,2,1,3,1,4,1,2,1,5,1,6,1,2,1,7,2,8,1,2,1,9,1,3,1,2,1,10,1,11,1,2,
%T A363486 1,3,1,12,1,2,1,13,1,14,1,2,1,15,1,4,3,2,1,16,2,3,1,2,1,17,1,18,1,2,1,
%U A363486 3,1,19,1,2,1,20,1,21,1,3,1,4,1,22,1,2,1
%N A363486 Low mode in the multiset of prime indices of n.
%C A363486 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A363486 A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes in {a,a,b,b,b,c,d,d,d} are {b,d}.
%C A363486 Extending the terminology of A124943, the "low mode" in a multiset is its least mode.
%t A363486 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363486 modes[ms_]:=Select[Union[ms],Count[ms,#]>=Max@@Length/@Split[ms]&];
%t A363486 Table[If[n==1,0,First[modes[prix[n]]]],{n,30}]
%Y A363486 Positions of first appearances are 1 and A000040.
%Y A363486 Positions of 1's are A360013, counted by A241131.
%Y A363486 For greatest instead of least we have A363487.
%Y A363486 The version for median is A363941, triangle A124943.
%Y A363486 The high version for median is A363942, triangle A124944.
%Y A363486 The version for mean instead of mode is A363943, high A363944.
%Y A363486 A112798 lists prime indices, length A001222, sum A056239.
%Y A363486 A326567/A326568 gives mean of prime indices.
%Y A363486 A359178 ranks partitions with a unique co-mode, counted by A362610.
%Y A363486 A356862 ranks partitions with a unique mode, counted by A362608.
%Y A363486 A362605 ranks partitions with more than one mode, counted by A362607.
%Y A363486 A362606 ranks partitions with more than one co-mode, counted by A362609.
%Y A363486 A362611 counts modes in prime indices, triangle A362614.
%Y A363486 A362613 counts co-modes in prime indices, triangle A362615.
%Y A363486 A362616 ranks partitions (max part) = (unique mode), counted by A362612.
%Y A363486 Cf. A000961, A215366, A327473, A327476, A360015, A363723.
%K A363486 nonn
%O A363486 1,3
%A A363486 _Gus Wiseman_, Jun 23 2023