A363223 - OEIS

%I #6 Jun 03 2023 23:56:43

%S 2,9,10,50,70,75,105,110,125,130,165,170,175,190,195,230,255,275,285,

%T 290,310,325,345,370,410,425,430,435,465,470,475,530,555,575,590,610,

%U 615,645,670,686,705,710,725,730,775,790,795,830,885,890,915,925,970

%N Numbers with bigomega equal to median prime index.

%C The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

%C 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.

%F 2*A001222(a(n)) = A360005(a(n)).

%e The terms together with their prime indices begin:

%e     2: {1}

%e     9: {2,2}

%e    10: {1,3}

%e    50: {1,3,3}

%e    70: {1,3,4}

%e    75: {2,3,3}

%e   105: {2,3,4}

%e   110: {1,3,5}

%e   125: {3,3,3}

%e   130: {1,3,6}

%e   165: {2,3,5}

%e   170: {1,3,7}

%e   175: {3,3,4}

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[1000],PrimeOmega[#]==Median[prix[#]]&]

%Y For maximum instead of median we have A106529, counted by A047993.

%Y For minimum instead of median we have A324522, counted by A006141.

%Y Partitions of this type are counted by A361800.

%Y For twice median we have A362050, counted by A362049.

%Y For maximum instead of length we have A362621, counted by A053263.

%Y A000975 counts subsets with integer median.

%Y A027746 lists prime factors, A112798 indices, length A001222, sum A056239.

%Y A325347 counts partitions with integer median, complement A307683.

%Y A359893 and A359901 count partitions by median.

%Y A359908 lists numbers whose prime indices have integer median.

%Y A360005 gives twice median of prime indices.

%Y Cf. A000040, A013580, A079309, A240219, A327473, A327476, A361860, A362619, A362622, A362980.

%K nonn

%O 1,1

%A _Gus Wiseman_, May 29 2023