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

2,1

Comments

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

a(n) = n iff n is prime.

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A079866 A134332 A276632 * A080210 A126594 A363895

Adjacent sequences: A273285 A273286 A273287 * A273289 A273290 A273291

Keyword

nonn

Author

Giuseppe Coppoletta, May 25 2016

Status

approved