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A273282 Largest prime not exceeding the geometric mean of all prime divisors of n counted with multiplicity.

%I A273282 #27 May 25 2016 17:10:36
%S A273282 2,3,2,5,2,7,2,3,3,11,2,13,3,3,2,17,2,19,2,3,3,23,2,5,5,3,3,29,3,31,2,
%T A273282 5,5,5,2,37,5,5,2,41,3,43,3,3,5,47,2,7,3,7,3,53,2,7,2,7,7,59,2,61,7,3,
%U A273282 2,7,3,67,3,7,3,71,2,73,7,3,3,7,3,79,2,3,7
%N A273282 Largest prime not exceeding the geometric mean of all prime divisors of n counted with multiplicity.
%C A273282 a(n) = n iff n is prime.
%C A273282 a(n) <= A079866(n) with equality iff A079866(n) is prime.
%H A273282 Giuseppe Coppoletta, <a href="/A273282/b273282.txt">Table of n, a(n) for n = 2..10000</a>
%F A273282 For n>=2, a(n) = A007917(A079866(n)).
%e A273282 a(46) = 5 because 5 is the greatest prime not bigger than sqrt(2*23).
%e A273282 For n = 5^3 * 11 * 89, a(n)=7 and A273283(n)=11 because A001222(n)=5 and 7 < n^(1/5) < 11.
%t A273282 a[n_] := NextPrime[ Floor[n^ (1/PrimeOmega[n])] + 1, -1]; a /@ Range[2, 100] (* _Giovanni Resta_, May 25 2016 *)
%o A273282 (Sage) [previous_prime(floor(n^(1/sloane.A001222(n)))+1) for n in (2..100)]
%o A273282 (PARI) a(n) = precprime(sqrtnint(n, bigomega(n))); \\ _Michel Marcus_, May 24 2016
%Y A273282 Cf. A273283, A273284, A273288, A079866, A001222.
%K A273282 nonn
%O A273282 2,1
%A A273282 _Giuseppe Coppoletta_, May 19 2016