A360556 Numbers > 1 whose first differences of 0-prepended prime indices have integer median.

2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 26, 27, 28, 29, 30, 31, 32, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84, 86, 87, 89

Offset

1,1

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..67.

Example

The 0-prepended prime indices of 1617 are {0,2,4,4,5}, with sorted differences {0,1,2,2}, with median 3/2, so 1617 is not in the sequence.

Mathematica

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 100], IntegerQ[Median[Differences[Prepend[prix[#], 0]]]]&]

Crossrefs

For mean instead of median we have A340610.

Positions of even terms in A360555.

The complement is A360557 (without 1).

These partitions are counted by A360688.

- For divisors (A063655) we have A139711, complement A139710.

- For prime indices (A360005) we have A359908, complement A359912.

- For distinct prime indices (A360457) we have A360550, complement A360551.

- For distinct prime factors (A360458) we have A360552, complement A100367.

- For prime factors (A360459) we have A359913, complement A072978.

- For prime multiplicities (A360460) we have A360553, complement A360554.

- For 0-prepended differences (A360555) we have A360556, complement A360557.

A112798 lists prime indices, length A001222, sum A056239.

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

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

A360614/A360615 = mean of first differences of 0-prepended prime indices.

Cf. A000975, A026424, A078175, A316413, A360009, A360558, A360669, A360681.

Sequence in context: A047256 A039252 A332484 * A039194 A242485 A099354

Adjacent sequences: A360553 A360554 A360555 * A360557 A360558 A360559

Keyword

nonn

Author

Gus Wiseman, Feb 16 2023

Status

approved