A273288 Largest prime not exceeding the median of all prime divisors of n counted with multiplicity.

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

Offset: 2

Author

Giuseppe Coppoletta, May 25 2016

Keywords

• nonn

Comments

A020639(n)<= a(n)<= A273289(n).

a(n) = n iff n is prime.

Examples

			a(66) = 3 because the median of [2, 3, 11] is the central value 3 (and it is prime).
a(308) = 3 because the median of [2, 2, 7, 11] is (2+7)/2 = 4.5 and the previous prime is 3.
		

Links

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

Crossrefs

Cf. A273282, A273284, A273289, A273290, A079866, A020639.

Programs

Mathematica

Table[Prime@ PrimePi@ 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])]; [previous_prime(floor(median(r(n)))+1) for n in (2..100)]