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

6, 12, 14, 15, 18, 24, 26, 28, 33, 35, 36, 38, 45, 48, 51, 52, 54, 56, 58, 65, 69, 72, 74, 75, 76, 77, 86, 93, 95, 96, 98, 99, 104, 106, 108, 112, 116, 119, 122, 123, 135, 141, 142, 143, 144, 145, 148, 152, 153, 158, 161, 162, 172, 175, 177, 178, 185, 192, 196

Offset: 1

Author

Gus Wiseman, Feb 16 2023

Keywords

• nonn

Comments

First differs from A325700 in having 330 and lacking 462.

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.

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 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.
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.
		

Crossrefs

For mean instead of median we have the complement of A326621.

Positions of odd terms in A360457.

The complement (without 1) is A360550, counted by A360686.

- 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.

A304038 lists distinct prime indices, length A001221, sum A066328.

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, A316413, A348551, A360006, A360009, A360248, A360453.

Programs

Mathematica

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