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

%I A273288 #19 Jun 03 2016 15:05:56
%S A273288 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,
%T A273288 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,
%U A273288 13,3,2,7,3,67,2,13,5,71,2,73,19,5,2,7,3,79,2,3,19
%N A273288 Largest prime not exceeding the median of all prime divisors of n counted with multiplicity.
%C A273288 A020639(n)<= a(n)<= A273289(n).
%C A273288 a(n) = n iff n is prime.
%H A273288 Giuseppe Coppoletta, <a href="/A273288/b273288.txt">Table of n, a(n) for n = 2..10000</a>
%e A273288 a(66) = 3 because the median of [2, 3, 11] is the central value 3 (and it is prime).
%e A273288 a(308) = 3 because the median of [2, 2, 7, 11] is (2+7)/2 = 4.5 and the previous prime is 3.
%t A273288 Table[Prime@ PrimePi@ Median@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ n, 1], {n, 2, 82}] (* _Michael De Vlieger_, May 27 2016 *)
%o A273288 (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)]
%Y A273288 Cf. A273282, A273284, A273289, A273290, A079866, A020639.
%K A273288 nonn
%O A273288 2,1
%A A273288 _Giuseppe Coppoletta_, May 25 2016