

A273288


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


4



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
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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 A086765
Adjacent sequences: A273285 A273286 A273287 * A273289 A273290 A273291


KEYWORD

nonn


AUTHOR

Giuseppe Coppoletta, May 25 2016


STATUS

approved



