cp's OEIS Frontend

A359912 Numbers whose prime indices do not have integer median.

%I A359912 #7 Jan 25 2023 09:09:04
%S A359912 1,6,14,15,26,33,35,36,38,51,58,60,65,69,74,77,84,86,93,95,106,119,
%T A359912 122,123,132,141,142,143,145,150,156,158,161,177,178,185,196,201,202,
%U A359912 204,209,210,214,215,216,217,219,221,225,226,228,249,262,265,276,278
%N A359912 Numbers whose prime indices do not have integer median.
%C A359912 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 A359912 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 A359912 The terms together with their prime indices begin:
%e A359912    1: {}
%e A359912    6: {1,2}
%e A359912   14: {1,4}
%e A359912   15: {2,3}
%e A359912   26: {1,6}
%e A359912   33: {2,5}
%e A359912   35: {3,4}
%e A359912   36: {1,1,2,2}
%e A359912   38: {1,8}
%e A359912   51: {2,7}
%e A359912   58: {1,10}
%e A359912   60: {1,1,2,3}
%t A359912 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A359912 Select[Range[100],!IntegerQ[Median[prix[#]]]&]
%Y A359912 For prime factors instead of indices we have A072978, complement A359913.
%Y A359912 These partitions are counted by A307683.
%Y A359912 For mean instead of median: A348551, complement A316413, counted by A349156.
%Y A359912 The complement is A359908, counted by A325347.
%Y A359912 Positions of odd terms in A360005.
%Y A359912 A112798 lists prime indices, length A001222, sum A056239.
%Y A359912 A326567/A326568 gives the mean of prime indices, conjugate A326839/A326840.
%Y A359912 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A359912 Cf. A026424, A051293, A067538, A175352, A175761, A289509, A359890, A359905, A360006, A359907, A360009.
%K A359912 nonn
%O A359912 1,2
%A A359912 _Gus Wiseman_, Jan 24 2023