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

1,1

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).

Links

Table of n, a(n) for n=1..66.

Example

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.

Mathematica

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

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.

Sequence in context: A175418 A078175 A213715 * A078174 A174894 A275616

Adjacent sequences: A360549 A360550 A360551 * A360553 A360554 A360555

Keyword

nonn

Author

Gus Wiseman, Feb 16 2023

Status

approved