A273283 Least prime not less than the geometric mean of all prime divisors of n counted with multiplicity.

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

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 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)]

Crossrefs

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

Sequence in context: A088387 A197861 A180506 * A359612 A276440 A162325

Adjacent sequences: A273280 A273281 A273282 * A273284 A273285 A273286

Keyword

nonn

Author

Giuseppe Coppoletta, May 19 2016

Status

approved