A360552 Numbers > 1 whose distinct prime factors have integer median.

2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 35, 37, 39, 41, 42, 43, 45, 47, 49, 51, 53, 55, 57, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 77, 78, 79, 81, 83, 84, 85, 87, 89, 90, 91, 93, 95, 97, 99, 101, 102, 103

Offset: 1

Author

Gus Wiseman, Feb 16 2023

Keywords

• nonn

Comments

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 prime factors of 900 are {2,2,3,3,5,5}, with distinct parts {2,3,5}, with median 3, so 900 is in the sequence.
		

Crossrefs

For mean instead of median we have A078174, complement of A176587.

The complement is A100367 (without 1).

Positions of even terms in A360458.

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

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

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

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

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

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

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

A027746 lists prime factors, length A001222, indices A112798.

A027748 lists distinct prime factors, length A001221, indices A304038.

A323171/A323172 = mean of distinct prime factors, indices A326619/A326620.

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

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

Cf. A000975, A026424, A056239, A078175, A175352, A316413, A326621, A360009.

Programs

Mathematica

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