A166123 - OEIS

%I #15 Aug 02 2019 23:00:37

%S 1,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,5,1,3,1,1,1,1,1,3,1,

%T 1,1,1,1,3,1,1,1,1,1,15,1,1,1,7,1,3,1,1,1,1,1,3,1,1,1,1,1,3,1,5,1,1,1,

%U 3,1,1,1,1,1,3,1,1,1,1,1,3,1,1,1,5,1,3,1,1,1,7,1,3,1,1,1,1,1,3,1

%N If n is prime, a(n) = 1; otherwise, a(n) is gcd(n, d) where d is the denominator of the (n-1)-th Bernoulli number.

%H Antti Karttunen, <a href="/A166123/b166123.txt">Table of n, a(n) for n = 1..21218</a>

%F a(n) = A166120(n)/ A050932(n-1).

%t Table[If[PrimeQ[n],1,GCD[n,Denominator[BernoulliB[n-1]]]],{n,100}] (* _Harvey P. Dale_, Sep 07 2017 *)

%o (PARI) a(n)=if(isprime(n),1,gcd(denominator(bernfrac(n-1)),n)) \\ _Charles R Greathouse IV_, Jun 20 2011

%o (PARI) a(n)=my(b=bernfrac(n-1));denominator(b)/denominator(b*n)/if(isprime(n),n,1) \\ _Charles R Greathouse IV_, Jun 20 2011

%o (PARI) a(n)=if(isprime(n),1,my(b=bernfrac(n-1));denominator(b)/denominator(b*n)) \\ _Charles R Greathouse IV_, Jun 20 2011

%Y Cf. A166062, A027642.

%K nonn

%O 1,9

%A _Paul Curtz_, Oct 07 2009