A386007 Least k such that there are exactly n primes that are popular on the interval [2,k] (see A385503); i.e., exactly n primes share the lead as the most common greatest prime factor of the numbers 2..k.

2, 3, 70, 2626355

Offset: 1

Author

Pontus von Brömssen, Jul 14 2025

Keywords

• nonn
• hard
• more

Examples

			a(3) = 70, because the 3 primes 3, 5, and 7 all occur A385652(70) = 10 times (the maximum) as the greatest prime factor of the numbers 2..70, and for earlier intervals there is never a tie between 3 numbers.
a(4) = 2626355, because the 4 primes 73, 83, 109, and 113 all occur A385652(2626355) = 7634 times (the maximum) as the greatest prime factor of the numbers 2..2626355, and for earlier intervals there is never a tie between 4 numbers.
		

Crossrefs

Cf. A006530, A385503, A385652.

Programs

Mathematica

gpf[n_]:=FactorInteger[n][[-1,1]];a[n_]:=Module[{k=1},Until[Length[Commonest[gpf/@Range[2,k]]]==n,k++];k] (* James C. McMahon, Jul 20 2025 *)