cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A360551 Numbers > 1 whose distinct prime indices have non-integer median.

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%I A360551 #7 Feb 16 2023 09:44:43
%S A360551 6,12,14,15,18,24,26,28,33,35,36,38,45,48,51,52,54,56,58,65,69,72,74,
%T A360551 75,76,77,86,93,95,96,98,99,104,106,108,112,116,119,122,123,135,141,
%U A360551 142,143,144,145,148,152,153,158,161,162,172,175,177,178,185,192,196
%N A360551 Numbers > 1 whose distinct prime indices have non-integer median.
%C A360551 First differs from A325700 in having 330 and lacking 462.
%C A360551 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. Distinct prime indices are listed by A304038.
%C A360551 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 A360551 The prime indices of 900 are {1,1,2,2,3,3}, with distinct parts {1,2,3}, with median 2, so 900 is not in the sequence.
%e A360551 The prime indices of 462 are {1,2,4,5}, with distinct parts {1,2,4,5}, with median 3, so 462 is not in the sequence.
%t A360551 Select[Range[2,100],!IntegerQ[Median[PrimePi/@First/@FactorInteger[#]]]&]
%Y A360551 For mean instead of median we have the complement of A326621.
%Y A360551 Positions of odd terms in A360457.
%Y A360551 The complement (without 1) is A360550, counted by A360686.
%Y A360551 - For divisors (A063655) we have A139710, complement A139711.
%Y A360551 - For prime indices (A360005) we have A359912, complement A359908.
%Y A360551 - For distinct prime indices (A360457) we have A360551 complement A360550.
%Y A360551 - For distinct prime factors (A360458) we have A100367, complement A360552.
%Y A360551 - For prime factors (A360459) we have A072978, complement A359913.
%Y A360551 - For prime multiplicities (A360460) we have A360554, complement A360553.
%Y A360551 - For 0-prepended differences (A360555) we have A360557, complement A360556.
%Y A360551 A112798 lists prime indices, length A001222, sum A056239.
%Y A360551 A304038 lists distinct prime indices, length A001221, sum A066328.
%Y A360551 A325347 = partitions w/ integer median, complement A307683, strict A359907.
%Y A360551 A326619/A326620 gives mean of distinct prime indices.
%Y A360551 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360551 Cf. A000975, A026424, A316413, A348551, A360006, A360009, A360248, A360453.
%K A360551 nonn
%O A360551 1,1
%A A360551 _Gus Wiseman_, Feb 16 2023