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A360006
Least positive integer whose prime indices have median n/2. a(1) = 1.
27
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).
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.
Sequence in context: A120859 A253258 A098810 * A081469 A331441 A209664
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 24 2023
STATUS
approved