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

Author

Giuseppe Coppoletta, May 25 2016

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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)]