

A273283


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


4



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, 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, 11, 5, 2, 11, 5, 67, 5, 11, 5, 71, 3, 73, 11, 5, 5, 11, 5, 79, 3, 3, 11
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OFFSET

2,1


COMMENTS

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.


LINKS

Giuseppe Coppoletta, Table of n, a(n) for n = 2..10000


FORMULA

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


EXAMPLE

a(46)=7 because 7 is the least prime not lesser than sqrt(2*23).
a(84)=5 and A273282(84)=3 because A001222(84)=4 and 3 < 84^(1/4) < 5.


MATHEMATICA

Table[NextPrime[(Ceiling[n^(1/PrimeOmega[n])]  1)], {n, 2, 50} ] (* G. C. Greubel, May 26 2016 *)


PROG

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


CROSSREFS

Cf. A273282, A273285, A273289, A079870, A079871, A006530, A001222.
Sequence in context: A088387 A197861 A180506 * A276440 A162325 A197862
Adjacent sequences: A273280 A273281 A273282 * A273284 A273285 A273286


KEYWORD

nonn


AUTHOR

Giuseppe Coppoletta, May 19 2016


STATUS

approved



