A360550 Numbers > 1 whose distinct prime indices have integer median.

2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 32, 34, 37, 39, 40, 41, 42, 43, 44, 46, 47, 49, 50, 53, 55, 57, 59, 60, 61, 62, 63, 64, 66, 67, 68, 70, 71, 73, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 94, 97, 100

Offset: 1

Author

Gus Wiseman, Feb 14 2023

Keywords

• nonn

Comments

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 in the sequence.
The prime indices of 330 are {1,2,3,5},  with distinct parts {1,2,3,5}, with median 5/2, so 330 is not in the sequence.
		

Crossrefs

For mean instead of median we have A326621.

Positions of even terms in A360457.

The complement (without 1) is A360551.

Partitions with these Heinz numbers are counted by A360686.

- 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.

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, A360006, A360009, A360248, A360453.

Programs

Mathematica

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