login
A273282
Largest prime not exceeding the geometric mean of all prime divisors of n counted with multiplicity.
4
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
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
KEYWORD
nonn
AUTHOR
Giuseppe Coppoletta, May 19 2016
STATUS
approved