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

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, 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, 2, 7, 3, 67, 3, 7, 3, 71, 2, 73, 7, 3, 3, 7, 3, 79, 2, 3, 7

Offset: 2

Author

Giuseppe Coppoletta, May 19 2016

Keywords

• nonn

Comments

a(n) = n iff n is prime.

a(n) <= A079866(n) with equality iff A079866(n) is prime.

Examples

			a(46) = 5 because 5 is the greatest prime not bigger than sqrt(2*23).
For n = 5^3 * 11 * 89, a(n)=7 and A273283(n)=11 because A001222(n)=5 and 7 < n^(1/5) < 11.
		

Links

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

Crossrefs

Cf. A273283, A273284, A273288, A079866, A001222.

Programs

Mathematica

a[n_] := NextPrime[ Floor[n^ (1/PrimeOmega[n])] + 1, -1]; a /@ Range[2, 100] (* Giovanni Resta, May 25 2016 *)

PARI

a(n) = precprime(sqrtnint(n, bigomega(n))); \\ Michel Marcus, May 24 2016

Sage

[previous_prime(floor(n^(1/sloane.A001222(n)))+1) for n in (2..100)]

Formula

For n>=2, a(n) = A007917(A079866(n)).