cp's OEIS Frontend

A363223 Numbers with bigomega equal to median prime index.

%I A363223 #6 Jun 03 2023 23:56:43
%S A363223 2,9,10,50,70,75,105,110,125,130,165,170,175,190,195,230,255,275,285,
%T A363223 290,310,325,345,370,410,425,430,435,465,470,475,530,555,575,590,610,
%U A363223 615,645,670,686,705,710,725,730,775,790,795,830,885,890,915,925,970
%N A363223 Numbers with bigomega equal to median prime index.
%C A363223 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 A363223 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 A363223 2*A001222(a(n)) = A360005(a(n)).
%e A363223 The terms together with their prime indices begin:
%e A363223     2: {1}
%e A363223     9: {2,2}
%e A363223    10: {1,3}
%e A363223    50: {1,3,3}
%e A363223    70: {1,3,4}
%e A363223    75: {2,3,3}
%e A363223   105: {2,3,4}
%e A363223   110: {1,3,5}
%e A363223   125: {3,3,3}
%e A363223   130: {1,3,6}
%e A363223   165: {2,3,5}
%e A363223   170: {1,3,7}
%e A363223   175: {3,3,4}
%t A363223 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A363223 Select[Range[1000],PrimeOmega[#]==Median[prix[#]]&]
%Y A363223 For maximum instead of median we have A106529, counted by A047993.
%Y A363223 For minimum instead of median we have A324522, counted by A006141.
%Y A363223 Partitions of this type are counted by A361800.
%Y A363223 For twice median we have A362050, counted by A362049.
%Y A363223 For maximum instead of length we have A362621, counted by A053263.
%Y A363223 A000975 counts subsets with integer median.
%Y A363223 A027746 lists prime factors, A112798 indices, length A001222, sum A056239.
%Y A363223 A325347 counts partitions with integer median, complement A307683.
%Y A363223 A359893 and A359901 count partitions by median.
%Y A363223 A359908 lists numbers whose prime indices have integer median.
%Y A363223 A360005 gives twice median of prime indices.
%Y A363223 Cf. A000040, A013580, A079309, A240219, A327473, A327476, A361860, A362619, A362622, A362980.
%K A363223 nonn
%O A363223 1,1
%A A363223 _Gus Wiseman_, May 29 2023