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

2,1

Comments

a(n) = n iff n is prime.

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(Sage) [previous_prime(floor(n^(1/sloane.A001222(n)))+1) for n in (2..100)]
(PARI) a(n) = precprime(sqrtnint(n, bigomega(n))); \\ Michel Marcus, May 24 2016

Crossrefs

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

Sequence in context: A091963 A067695 A285336 * A079866 A134332 A276632

Adjacent sequences: A273279 A273280 A273281 * A273283 A273284 A273285

Keyword

nonn

Author

Giuseppe Coppoletta, May 19 2016

Status

approved