A080213 a(n) = binomial(n, greatest prime factor of n).

1, 1, 1, 6, 1, 20, 1, 28, 84, 252, 1, 220, 1, 3432, 3003, 120, 1, 816, 1, 15504, 116280, 705432, 1, 2024, 53130, 10400600, 2925, 1184040, 1, 142506, 1, 496, 193536720, 2333606220, 6724520, 7140, 1, 35345263800, 8122425444, 658008, 1, 26978328, 1

Offset: 1

Author

Reinhard Zumkeller, Feb 06 2003

Keywords

• nonn

Comments

For n>1: a(n)=1 iff n is prime.

Links

• Robin Visser, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A006530, A080211, A080212.

Programs

Mathematica

Table[Binomial[n,FactorInteger[n][[-1,1]]],{n,50}] (* Harvey P. Dale, Feb 25 2015 *)

PARI

a(n) = if (n==1, 1, binomial(n, vecmax(factor(n)[,1]))); \\ Michel Marcus, May 06 2020

Sage

def a(n):
    if n==1: return 1
    return binomial(n, factor(n)[-1][0])  # Robin Visser, Nov 25 2023

Formula

a(n) = binomial(n, A006530(n)). - Michel Marcus, May 06 2020