A385503 Popular primes.

2, 3, 5, 7, 13, 19, 23, 31, 43, 47, 73, 83, 109, 113, 199, 283, 467, 661, 773, 887, 1109, 1129, 1327, 1627, 2143, 2399, 2477, 2803, 2861, 2971, 3739, 3931, 3947, 4297

Offset

1,1

Comments

McNew says that a prime p is "popular" on an interval [2, k] if no prime occurs more frequently than p as the greatest prime factor (gpf, A006530) of the integers in that interval. - N. J. A. Sloane, Jul 25 2017

Does there exist two popular primes p < q such that q gets popular earlier than p, i.e., such that q is popular (for the first time) on [2,k] but p is not popular on [2,j] for any j < k? - Pontus von Brömssen, Jul 02 2025

Links

Table of n, a(n) for n=1..34.

Nathan McNew, Popular values of the largest prime divisor function, arXiv:1504.05985 [math.NT], April 2015.

Nathan McNew, Popular values of the largest prime divisor function (corrected version), page 16, November 2015.

Nathan McNew, The Most Frequent Values of the Largest Prime Divisor Function, Exper. Math., 2017, Vol. 26, No. 2, 210-224.

Crossrefs

Cf. A006530, A124661, A246033.

Sequence in context: A387687 A385504 A124661 * A319126 A134266 A233043

Adjacent sequences: A385500 A385501 A385502 * A385504 A385505 A385506

Keyword

nonn,more

Author

Peter Munn, Jul 01 2025

Status

approved