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%I A360556 #9 Feb 16 2023 13:41:44
%S A360556 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 A360556 35,37,38,39,41,42,43,44,45,47,48,49,50,52,53,57,58,59,60,61,63,64,65,
%U A360556 66,67,68,70,71,72,73,74,75,76,78,79,80,81,83,84,86,87,89
%N A360556 Numbers > 1 whose first differences of 0-prepended prime indices have integer median.
%C A360556 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 A360556 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 A360556 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 A360556 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A360556 Select[Range[2,100],IntegerQ[Median[Differences[Prepend[prix[#],0]]]]&]
%Y A360556 For mean instead of median we have A340610.
%Y A360556 Positions of even terms in A360555.
%Y A360556 The complement is A360557 (without 1).
%Y A360556 These partitions are counted by A360688.
%Y A360556 - For divisors (A063655) we have A139711, complement A139710.
%Y A360556 - For prime indices (A360005) we have A359908, complement A359912.
%Y A360556 - For distinct prime indices (A360457) we have A360550, complement A360551.
%Y A360556 - For distinct prime factors (A360458) we have A360552, complement A100367.
%Y A360556 - For prime factors (A360459) we have A359913, complement A072978.
%Y A360556 - For prime multiplicities (A360460) we have A360553, complement A360554.
%Y A360556 - For 0-prepended differences (A360555) we have A360556, complement A360557.
%Y A360556 A112798 lists prime indices, length A001222, sum A056239.
%Y A360556 A325347 = partitions w/ integer median, complement A307683, strict A359907.
%Y A360556 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360556 A360614/A360615 = mean of first differences of 0-prepended prime indices.
%Y A360556 Cf. A000975, A026424, A078175, A316413, A360009, A360558, A360669, A360681.
%K A360556 nonn
%O A360556 1,1
%A A360556 _Gus Wiseman_, Feb 16 2023

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