A359912 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

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}

MATHEMATICA

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[100], !IntegerQ[Median[prix[#]]]&]

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.

Sequence in context: A341448 A081535 A355941 * A325698 A338907 A218005

Adjacent sequences: A359909 A359910 A359911 * A359913 A359914 A359915

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 24 2023

STATUS

approved