cp's OEIS Frontend

A359913 Numbers whose multiset of prime factors has integer median.

%I A359913 #5 Jan 26 2023 10:04:19
%S A359913 2,3,4,5,7,8,9,11,12,13,15,16,17,18,19,20,21,23,24,25,27,28,29,30,31,
%T A359913 32,33,35,37,39,40,41,42,43,44,45,47,48,49,50,51,52,53,54,55,56,57,59,
%U A359913 61,63,64,65,66,67,68,69,70,71,72,73,75,76,77,78,79,80,81
%N A359913 Numbers whose multiset of prime factors has integer median.
%C A359913 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%e A359913 The terms together with their prime factors begin:
%e A359913    2: {2}
%e A359913    3: {3}
%e A359913    4: {2,2}
%e A359913    5: {5}
%e A359913    7: {7}
%e A359913    8: {2,2,2}
%e A359913    9: {3,3}
%e A359913   11: {11}
%e A359913   12: {2,2,3}
%e A359913   13: {13}
%e A359913   15: {3,5}
%e A359913   16: {2,2,2,2}
%e A359913   17: {17}
%e A359913   18: {2,3,3}
%e A359913   19: {19}
%e A359913   20: {2,2,5}
%e A359913   21: {3,7}
%e A359913   23: {23}
%e A359913   24: {2,2,2,3}
%t A359913 Select[Range[2,100],IntegerQ[Median[Flatten[ConstantArray@@@FactorInteger[#]]]]&]
%Y A359913 Prime factors are listed by A027746.
%Y A359913 The complement is A072978, for prime indices A359912.
%Y A359913 For mean instead of median we have A078175, for prime indices A316413.
%Y A359913 For prime indices instead of factors we have A359908, counted by A325347.
%Y A359913 Positions of even terms in A360005.
%Y A359913 A067340 lists numbers whose prime signature has integer mean.
%Y A359913 A112798 lists prime indices, length A001222, sum A056239.
%Y A359913 A325347 counts partitions with integer median, strict A359907.
%Y A359913 A326567/A326568 gives the mean of prime indices, conjugate A326839/A326840.
%Y A359913 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A359913 Cf. A067538, A175352, A348551, A359890, A359905, A360007, A360006, A360069.
%K A359913 nonn
%O A359913 1,1
%A A359913 _Gus Wiseman_, Jan 25 2023