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Least prime not less than the geometric mean of all prime divisors of n counted with multiplicity.
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%I #31 Jan 21 2022 05:06:20

%S 2,3,2,5,3,7,2,3,5,11,3,13,5,5,2,17,3,19,3,5,5,23,3,5,7,3,5,29,5,31,2,

%T 7,7,7,3,37,7,7,3,41,5,43,5,5,7,47,3,7,5,11,5,53,3,11,3,11,11,59,3,61,

%U 11,5,2,11,5,67,5,11,5,71,3,73,11,5,5,11,5,79,3,3,11

%N Least prime not less than the geometric mean of all prime divisors of n counted with multiplicity.

%C A079870(n) <= a(n) <= A006530(n) <= n and a(n) = n iff n is prime, while a(n)= A079870(n) iff A079870(n) is prime.

%H Giuseppe Coppoletta, <a href="/A273283/b273283.txt">Table of n, a(n) for n = 2..10000</a>

%F For n >= 2, a(n) = A007918(A079870(n)).

%e a(46)=7 because 7 is the least prime not less than sqrt(2*23).

%e a(84)=5 and A273282(84)=3 because A001222(84)=4 and 3 < 84^(1/4) < 5.

%t Table[NextPrime[(Ceiling[n^(1/PrimeOmega[n])] - 1)], {n,2,50} ] (* _G. C. Greubel_, May 26 2016 *)

%o (Sage) [next_prime(ceil(n^(1/sloane.A001222(n)))-1) for n in (2..82)]

%Y Cf. A273282, A273285, A273289, A079870, A079871, A006530, A001222.

%K nonn

%O 2,1

%A _Giuseppe Coppoletta_, May 19 2016