proposed

approved

editing

proposed

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

allocated for Gus WisemanLeast 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

1,2

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).

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

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]}]

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 lists numbers whose prime indices have integer median, complement A359912.

Cf. A026424, A359889, A359890, A360009.

allocated

nonn

Gus Wiseman, Jan 24 2023

approved

editing

allocated for Gus Wiseman

allocated

approved