%I #7 Jan 25 2023 09:09:04
%S 1,6,14,15,26,33,35,36,38,51,58,60,65,69,74,77,84,86,93,95,106,119,
%T 122,123,132,141,142,143,145,150,156,158,161,177,178,185,196,201,202,
%U 204,209,210,214,215,216,217,219,221,225,226,228,249,262,265,276,278
%N Numbers whose prime indices do not have integer median.
%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.
%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).
%e The terms together with their prime indices begin:
%e 1: {}
%e 6: {1,2}
%e 14: {1,4}
%e 15: {2,3}
%e 26: {1,6}
%e 33: {2,5}
%e 35: {3,4}
%e 36: {1,1,2,2}
%e 38: {1,8}
%e 51: {2,7}
%e 58: {1,10}
%e 60: {1,1,2,3}
%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],!IntegerQ[Median[prix[#]]]&]
%Y For prime factors instead of indices we have A072978, complement A359913.
%Y These partitions are counted by A307683.
%Y For mean instead of median: A348551, complement A316413, counted by A349156.
%Y The complement is A359908, counted by A325347.
%Y Positions of odd terms in A360005.
%Y A112798 lists prime indices, length A001222, sum A056239.
%Y A326567/A326568 gives the mean of prime indices, conjugate A326839/A326840.
%Y A359893 and A359901 count partitions by median, odd-length A359902.
%Y Cf. A026424, A051293, A067538, A175352, A175761, A289509, A359890, A359905, A360006, A359907, A360009.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jan 24 2023
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