A359912 Numbers whose prime indices do not have integer median.

1, 6, 14, 15, 26, 33, 35, 36, 38, 51, 58, 60, 65, 69, 74, 77, 84, 86, 93, 95, 106, 119, 122, 123, 132, 141, 142, 143, 145, 150, 156, 158, 161, 177, 178, 185, 196, 201, 202, 204, 209, 210, 214, 215, 216, 217, 219, 221, 225, 226, 228, 249, 262, 265, 276, 278

Offset: 1

Author

Gus Wiseman, Jan 24 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 terms together with their prime indices begin:
   1: {}
   6: {1,2}
  14: {1,4}
  15: {2,3}
  26: {1,6}
  33: {2,5}
  35: {3,4}
  36: {1,1,2,2}
  38: {1,8}
  51: {2,7}
  58: {1,10}
  60: {1,1,2,3}
		

Crossrefs

For prime factors instead of indices we have A072978, complement A359913.

These partitions are counted by A307683.

For mean instead of median: A348551, complement A316413, counted by A349156.

The complement is A359908, counted by A325347.

Positions of odd terms in A360005.

A112798 lists prime indices, length A001222, sum A056239.

A326567/A326568 gives the mean of prime indices, conjugate A326839/A326840.

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

Cf. A026424, A051293, A067538, A175352, A175761, A289509, A359890, A359905, A360006, A359907, A360009.

Programs

Mathematica

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