cp's OEIS Frontend

A360248 Numbers for which the prime indices do not have the same median as the distinct prime indices.

%I A360248 #7 Feb 09 2023 20:49:19
%S A360248 12,18,20,24,28,40,44,45,48,50,52,54,56,60,63,68,72,75,76,80,84,88,92,
%T A360248 96,98,99,104,108,112,116,117,120,124,132,135,136,140,144,147,148,150,
%U A360248 152,153,156,160,162,164,168,171,172,175,176,184,188,189,192,200
%N A360248 Numbers for which the prime indices do not have the same median as the distinct prime indices.
%C A360248 First differs from A242416 in lacking 180, with prime indices {1,1,2,2,3}.
%C A360248 First differs from A360246 in lacking 126 and having 1950.
%C A360248 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 A360248 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 A360248 The terms together with their prime indices begin:
%e A360248   12: {1,1,2}
%e A360248   18: {1,2,2}
%e A360248   20: {1,1,3}
%e A360248   24: {1,1,1,2}
%e A360248   28: {1,1,4}
%e A360248   40: {1,1,1,3}
%e A360248   44: {1,1,5}
%e A360248   45: {2,2,3}
%e A360248   48: {1,1,1,1,2}
%e A360248   50: {1,3,3}
%e A360248   52: {1,1,6}
%e A360248   54: {1,2,2,2}
%e A360248   56: {1,1,1,4}
%e A360248   60: {1,1,2,3}
%e A360248   63: {2,2,4}
%e A360248   68: {1,1,7}
%e A360248   72: {1,1,1,2,2}
%e A360248 The prime indices of 126 are {1,2,2,4} with median 2 and distinct prime indices {1,2,4} with median 2, so 126 is not in the sequence.
%e A360248 The prime indices of 1950 are {1,2,3,3,6} with median 3 and distinct prime indices {1,2,3,6} with median 5/2, so 1950 is in the sequence.
%t A360248 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360248 Select[Range[100],Median[prix[#]]!=Median[Union[prix[#]]]&]
%Y A360248 These partitions are counted by A360244.
%Y A360248 The complement is A360249, counted by A360245.
%Y A360248 For multiplicities instead of parts: complement of A360453.
%Y A360248 For multiplicities instead of distinct parts: complement of A360454.
%Y A360248 For mean instead of median we have A360246, counted by A360242.
%Y A360248 The complement for mean instead of median is A360247, counted by A360243.
%Y A360248 A112798 lists prime indices, length A001222, sum A056239.
%Y A360248 A326567/A326568 gives mean of prime indices.
%Y A360248 A326619/A326620 gives mean of distinct prime indices.
%Y A360248 A325347 = partitions with integer median, strict A359907, ranked by A359908.
%Y A360248 A359893 and A359901 count partitions by median.
%Y A360248 A360005 gives median of prime indices (times two).
%Y A360248 Cf. A000975, A078174, A316413, A324570, A359890, A360455, A360456.
%K A360248 nonn
%O A360248 1,1
%A A360248 _Gus Wiseman_, Feb 07 2023