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A273289 Least prime not less than the median of all prime divisors of n counted with multiplicity.

%I A273289 #24 Jun 03 2016 14:59:17
%S A273289 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,
%T A273289 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,
%U A273289 59,3,61,17,3,2,11,3,67,2,13,5,71,2,73,23,5,2,11,3,79,2,3,23
%N A273289 Least prime not less than the median of all prime divisors of n counted with multiplicity.
%C A273289 A273288(n)<= a(n)<= A006530<= n and a(n) = n iff n is prime.
%H A273289 Giuseppe Coppoletta, <a href="/A273289/b273289.txt">Table of n, a(n) for n = 2..10000</a>
%e A273289 a(76) = 2 because the median of its prime factors [2, 2, 19] is the central value 2 (and it is prime).
%e A273289 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.
%t A273289 Table[If[PrimeQ@ #, #, NextPrime@ #] &@ Median@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ n, 1], {n, 2, 82}] (* _Michael De Vlieger_, May 27 2016 *)
%o A273289 (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)]
%Y A273289 Cf. A273283, A273285, A273288, A273291, A079870, A006530.
%K A273289 nonn
%O A273289 2,1
%A A273289 _Giuseppe Coppoletta_, May 25 2016