A166123 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.

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, 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, 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

Offset: 1

Author

Paul Curtz, Oct 07 2009

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..21218

Crossrefs

Cf. A166062, A027642.

Programs

Mathematica

Table[If[PrimeQ[n],1,GCD[n,Denominator[BernoulliB[n-1]]]],{n,100}] (* Harvey P. Dale, Sep 07 2017 *)

PARI

a(n)=if(isprime(n),1,gcd(denominator(bernfrac(n-1)),n)) \\ Charles R Greathouse IV, Jun 20 2011

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

PARI

a(n)=if(isprime(n),1,my(b=bernfrac(n-1));denominator(b)/denominator(b*n)) \\ Charles R Greathouse IV, Jun 20 2011

Formula

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