%I #9 Feb 16 2023 13:41:44

%S 2,3,5,6,7,8,9,11,12,13,14,16,17,18,19,20,21,23,26,27,28,29,30,31,32,

%T 35,37,38,39,41,42,43,44,45,47,48,49,50,52,53,57,58,59,60,61,63,64,65,

%U 66,67,68,70,71,72,73,74,75,76,78,79,80,81,83,84,86,87,89

%N Numbers > 1 whose first differences of 0-prepended prime indices 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 0-prepended prime indices of 1617 are {0,2,4,4,5}, with sorted differences {0,1,2,2}, with median 3/2, so 1617 is not in the sequence.

%t prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[2,100],IntegerQ[Median[Differences[Prepend[prix[#],0]]]]&]

%Y For mean instead of median we have A340610.

%Y Positions of even terms in A360555.

%Y The complement is A360557 (without 1).

%Y These partitions are counted by A360688.

%Y - For divisors (A063655) we have A139711, complement A139710.

%Y - For prime indices (A360005) we have A359908, complement A359912.

%Y - For distinct prime indices (A360457) we have A360550, complement A360551.

%Y - For distinct prime factors (A360458) we have A360552, complement A100367.

%Y - For prime factors (A360459) we have A359913, complement A072978.

%Y - For prime multiplicities (A360460) we have A360553, complement A360554.

%Y - For 0-prepended differences (A360555) we have A360556, complement A360557.

%Y A112798 lists prime indices, length A001222, sum A056239.

%Y A325347 = partitions w/ integer median, complement A307683, strict A359907.

%Y A359893 and A359901 count partitions by median, odd-length A359902.

%Y A360614/A360615 = mean of first differences of 0-prepended prime indices.

%Y Cf. A000975, A026424, A078175, A316413, A360009, A360558, A360669, A360681.

%K nonn

%O 1,1

%A _Gus Wiseman_, Feb 16 2023