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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
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
FORMULA
For n >= 2, a(n) = A007918(A079870(n)).
EXAMPLE
a(46)=7 because 7 is the least prime not less 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)]
KEYWORD
nonn
AUTHOR
Giuseppe Coppoletta, May 19 2016
STATUS
approved