A080211 a(n) = binomial(n, smallest prime factor of n).

1, 1, 1, 6, 1, 15, 1, 28, 84, 45, 1, 66, 1, 91, 455, 120, 1, 153, 1, 190, 1330, 231, 1, 276, 53130, 325, 2925, 378, 1, 435, 1, 496, 5456, 561, 324632, 630, 1, 703, 9139, 780, 1, 861, 1, 946, 14190, 1035, 1, 1128, 85900584, 1225, 20825, 1326, 1, 1431, 3478761

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..10000

Crossrefs

Cf. A020639, A080212, A080213.

Programs

Mathematica

Table[Binomial[n,FactorInteger[n][[1,1]]],{n,60}]  (* Harvey P. Dale, Apr 12 2011 *)

PARI

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

Sage

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

Formula

a(n) = binomial(n, A020639(n)). - Michel Marcus, May 06 2020