A360458 Two times the median of the set of distinct prime factors of n; a(1) = 2.

2, 4, 6, 4, 10, 5, 14, 4, 6, 7, 22, 5, 26, 9, 8, 4, 34, 5, 38, 7, 10, 13, 46, 5, 10, 15, 6, 9, 58, 6, 62, 4, 14, 19, 12, 5, 74, 21, 16, 7, 82, 6, 86, 13, 8, 25, 94, 5, 14, 7, 20, 15, 106, 5, 16, 9, 22, 31, 118, 6, 122, 33, 10, 4, 18, 6, 134, 19, 26, 10, 142, 5

Offset: 1

Author

Gus Wiseman, Feb 14 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). Since the denominator is always 1 or 2, the median can be represented as an integer by multiplying by 2.

Examples

			The prime factors of 336 are {2,2,2,2,3,7}, with distinct parts {2,3,7}, with median 3, so a(336) = 6.
		

Crossrefs

The union is 2 followed by A014091, complement of A014092.

Distinct prime factors are listed by A027748.

The version for divisors is A063655.

Positions of odd terms are A100367.

For mean instead of two times median we have A323171/A323172.

The version for prime indices is A360005.

The version for distinct prime indices is A360457.

The version for prime factors is A360459.

The version for prime multiplicities is A360460.

Positions of even terms are A360552.

The version for 0-prepended differences is A360555.

A112798 lists prime indices, length A001222, sum A056239.

A304038 lists distinct prime indices.

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

Cf. A000975, A026424, A078174, A316413, A325347, A359907, A360006, A360248, A360453, A360550, A360551.

Programs

Mathematica

Table[2*Median[First/@FactorInteger[n]],{n,100}]