%I
%S 1,3,5,3,2,3,11,3,13,7,2,17,19,5,7,11,3,5,3,7,29,5,2,11,17,7,3,37,13,
%T 5,7,43,11,5,23,47,7,5,17,13,3,11,19,29,59,5,31,7,2,13,11,67,23,7,71,
%U 3,73,37,19,11,79,5,3,41,83,7,43,29,11,89,13,23,47,19,3,97,7,11,101,17,103
%N Greatest prime factor in A095117(n) = greatest prime factor in n + pi(n) where pi(n) is the prime counting function = greatest prime factor in n + A000720(n).
%C Conjecture: every prime appears infinitely often in this sequence.
%D Guy, R. K. "The Largest Prime Factor of n." B46 in Unsolved Problems in Number Theory, 2nd ed. New York: SpringerVerlag, p. 101, 1994.
%D Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993.
%H Andrew Booker, <a href="http://primes.utm.edu/nthprime/index.php#piofx">The Nth Prime Page</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">"Prime Counting Function."</a>
%F a(n) = A006530(n + A000720(n)) = greatest prime factor in (n + A000720(n)).
%e a(1) = 1 = A006530(1+0).
%e a(3) = 5 because 3 + pi(3) = p + number of primes less than or equal to 3, of which there are 2 (namely 2 and 3) hence a(3) = 3 + 2 = 5. This is prime, hence equal to its greatest prime factor. a(5) = 2 because 5 + pi(5) = 5 + 3 = 2 * 2 * 2 hence the greatest prime factor is 2.
%Y Cf. A000720, A006530, A095117.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Nov 22 2004
%E Extended by _Ray Chandler_, Nov 27 2004
