

A273289


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


4



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
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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: A086287 A253236 A286516 * A090662 A088387 A197861
Adjacent sequences: A273286 A273287 A273288 * A273290 A273291 A273292


KEYWORD

nonn


AUTHOR

Giuseppe Coppoletta, May 25 2016


STATUS

approved



