A360554 Numbers > 1 whose unordered prime signature has non-integer median.

12, 18, 20, 28, 44, 45, 48, 50, 52, 63, 68, 72, 75, 76, 80, 92, 98, 99, 108, 112, 116, 117, 124, 147, 148, 153, 162, 164, 171, 172, 175, 176, 188, 192, 200, 207, 208, 212, 236, 242, 244, 245, 261, 268, 272, 275, 279, 284, 288, 292, 304, 316, 320, 325, 332, 333

Offset: 1

Author

Gus Wiseman, Feb 16 2023

Keywords

• nonn

Comments

First differs from A187039 in having 2520 and lacking 1 and 12600.

A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.

The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).

Examples

			The unordered prime signature of 2520 is {3,2,1,1}, with median 3/2, so 2520 is in the sequence.
The unordered prime signature of 12600 is {3,2,2,1}, with median 2, so 12600 is not in the sequence.
		

Crossrefs

A subset of A030231.

For mean instead of median we have A070011.

Positions of odd terms in A360460.

The complement is A360553 (without 1), counted by A360687.

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

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

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

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

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

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

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

A112798 lists prime indices, length A001222, sum A056239.

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

A326619/A326620 gives mean of distinct prime indices.

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

Cf. A000975, A026424, A304038, A316413, A326621, A348551, A360006, A360009, A360248, A360453.

Programs

Mathematica

Select[Range[2,100],!IntegerQ[Median[Last/@FactorInteger[#]]]&]