A273289 Least prime not less than the median of all prime divisors of n counted with multiplicity.

2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 2, 13, 5, 5, 2, 17, 3, 19, 2, 5, 7, 23, 2, 5, 11, 3, 2, 29, 3, 31, 2, 7, 11, 7, 3, 37, 11, 11, 2, 41, 3, 43, 2, 3, 13, 47, 2, 7, 5, 11, 2, 53, 3, 11, 2, 11, 17, 59, 3, 61, 17, 3, 2, 11, 3, 67, 2, 13, 5, 71, 2, 73, 23, 5, 2, 11, 3, 79, 2, 3, 23

Offset

2,1

Comments

A273288(n)<= a(n)<= A006530<= n and a(n) = n iff n is prime.

Links

Giuseppe Coppoletta, Table of n, a(n) for n = 2..10000

Example

a(76) = 2 because the median of its prime factors [2, 2, 19] is the central value 2 (and it is prime).
a(308) = 5 because the median of [2, 2, 7, 11] is commonly defined as the mean of the central values (2+7)/2 = 4.5 and the next prime is 5.

Mathematica

Table[If[PrimeQ@ #, #, NextPrime@ #] &@ Median@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ n, 1], {n, 2, 82}] (* Michael De Vlieger, May 27 2016 *)

Prog

(Sage) r = lambda n: [f[0] for f in factor(n) for _ in range(f[1])]; [next_prime(ceil(median(r(n)))-1) for n in (2..100)]

Crossrefs

Cf. A273283, A273285, A273288, A273291, A079870, A006530.

Sequence in context: A253236 A342257 A286516 * A365521 A361725 A356840

Adjacent sequences: A273286 A273287 A273288 * A273290 A273291 A273292

Keyword

nonn

Author

Giuseppe Coppoletta, May 25 2016

Status

approved