A360006 Least positive integer whose prime indices have median n/2. a(1) = 1.

1, 2, 6, 3, 14, 5, 26, 7, 38, 11, 58, 13, 74, 17, 86, 19, 106, 23, 122, 29, 142, 31, 158, 37, 178, 41, 202, 43, 214, 47, 226, 53, 262, 59, 278, 61, 302, 67, 326, 71, 346, 73, 362, 79, 386, 83, 398, 89, 446, 97, 458, 101, 478, 103, 502, 107, 526, 109, 542, 113

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..60.

Formula

Consists of 1 followed by A000040 interleaved with 2*A031215.

Mathematica

nn=100;
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
seq=Table[If[n==1, 1, 2*Median[prix[n]]], {n, nn}];
Table[Position[seq, k][[1, 1]], {k, Count[Differences[Union[seq]], 1]}]

Crossrefs

Position of first appearance of n in A360005.

The sorted version is A360007, for mean A360008.

A112798 lists prime indices, length A001222, sum A056239.

A316413 lists numbers whose prime indices have integer mean.

A325347 = partitions w/ integer median, strict A359907, complement A307683.

A326567/A326568 gives mean of prime indices.

A359893 counts partitions by median, cf. A359901, A359902.

A359908 = numbers w/ integer median of prime indices, complement A359912.

Cf. A026424, A359889, A359890, A360009.

Sequence in context: A120859 A253258 A098810 * A081469 A331441 A209664

Adjacent sequences: A360003 A360004 A360005 * A360007 A360008 A360009

Keyword

nonn

Author

Gus Wiseman, Jan 24 2023

Status

approved