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a(n) = binomial(n, smallest prime factor of n).
5

%I #17 Nov 25 2023 07:29:34

%S 1,1,1,6,1,15,1,28,84,45,1,66,1,91,455,120,1,153,1,190,1330,231,1,276,

%T 53130,325,2925,378,1,435,1,496,5456,561,324632,630,1,703,9139,780,1,

%U 861,1,946,14190,1035,1,1128,85900584,1225,20825,1326,1,1431,3478761

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

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

%H Robin Visser, <a href="/A080211/b080211.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = binomial(n, A020639(n)). - _Michel Marcus_, May 06 2020

%t Table[Binomial[n,FactorInteger[n][[1,1]]],{n,60}] (* _Harvey P. Dale_, Apr 12 2011 *)

%o (PARI) a(n) = if (n==1, 1, binomial(n, vecmin(factor(n)[,1]))); \\ _Michel Marcus_, May 06 2020

%o (Sage)

%o def a(n):

%o if n==1: return 1

%o return binomial(n, factor(n)[0][0]) # _Robin Visser_, Nov 25 2023

%Y Cf. A020639, A080212, A080213.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Feb 06 2003