A360557 Numbers > 1 whose sorted first differences of 0-prepended prime indices have non-integer median.

4, 10, 15, 22, 24, 25, 33, 34, 36, 40, 46, 51, 54, 55, 56, 62, 69, 77, 82, 85, 88, 93, 94, 100, 104, 115, 118, 119, 121, 123, 134, 135, 136, 141, 146, 152, 155, 161, 166, 177, 184, 187, 194, 196, 201, 205, 206, 217, 218, 219, 220, 221, 225, 232, 235, 240, 248

Offset: 1

Author

Gus Wiseman, Feb 17 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.

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 0-prepended prime indices of 1617 are {0,2,4,4,5}, with sorted differences {0,1,2,2}, with median 3/2, so 1617 is in the sequence.
		

Crossrefs

For mean instead of median complement we have A340610, counted by A168659.

For mean instead of median we have A360668, counted by A200727.

Positions of odd terms in A360555.

The complement is A360556 (without 1), counted by A360688.

These partitions are counted by A360691.

- 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.

A287352 lists 0-prepended first differences of prime indices.

A325347 counts partitions with integer median, complement A307683.

A355536 lists first differences of prime indices.

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

A360614/A360615 = mean of first differences of 0-prepended prime indices.

Cf. A000975, A026424, A078175, A316413, A360009, A360558, A360669, A360681.

Programs

Mathematica

prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[2,100],!IntegerQ[Median[Differences[Prepend[prix[#],0]]]]&]