A100194 Incrementally largest denominators of the Bernoulli numbers.

1, 2, 6, 30, 42, 66, 2730, 14322, 1919190, 56786730, 140100870, 209191710, 2328255930, 2381714790, 7225713885390, 9538864545210, 21626561658972270, 446617991732222310, 115471236091149548610, 5145485882746933233510, 14493038256293268734790

Offset: 1

Author

Eric W. Weisstein, Nov 08 2004

Keywords

• nonn

Links

• Daniel Suteu, Table of n, a(n) for n = 1..85
• Eric Weisstein's World of Mathematics, Bernoulli Number
• Wikipedia, Von Staudt-Clausen theorem

Crossrefs

Cf. A100195, A000367/A002445.

Programs

Mathematica

Reap[For[n = record = 0, n < 1000, n = n + 2, If[(d = Denominator[BernoulliB[n]]) > record, Sow[d]; record = d]]][[2, 1]] (* Jean-François Alcover, Nov 09 2012 *)

PARI

b(n) = if((n==0) || (n>1 && n%2==1), 1, my(d=divisors(n)); prod(k=1, #d, if(isprime(d[k]+1), d[k]+1, 1))); \\ more efficient than denominator(bernfrac(n))
lista(n) = { my(m=0); for(k=0, n, my(d=b(k)); if(d>m, m=d; print1(d, ", "))); }
lista(1000); \\ Daniel Suteu, Dec 22 2018

Extensions

a(21) from Seiichi Manyama, Jan 21 2017