A100195 Numbers n such that the denominator of BernoulliB(n) is a record.

0, 1, 2, 4, 6, 10, 12, 30, 36, 60, 72, 108, 120, 144, 180, 240, 360, 420, 540, 840, 1008, 1080, 1200, 1260, 1620, 1680, 2016, 2160, 2520, 3360, 3780, 5040, 6480, 7560, 8400, 10080, 12600, 15120, 25200, 30240, 42840, 45360, 55440, 60480, 75600, 85680, 100800

Offset: 1

Author

Eric W. Weisstein, Nov 08 2004

Keywords

• nonn

Links

• Daniel Suteu, Table of n, a(n) for n = 1..90
• Eric Weisstein's World of Mathematics, Bernoulli Number
• Wikipedia, Von Staudt-Clausen theorem

Crossrefs

Cf. A100194 (the corresponding Bernoulli denominators), A000367/A002445.

Programs

Mathematica

DeleteDuplicates[Table[{n,Denominator[BernoulliB[n]]},{n,0,101000}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]] (* Harvey P. Dale, Jul 22 2025 *)

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(k, ", "))); }
lista(100000); \\ Daniel Suteu, Dec 23 2018

Extensions

Corrected and extended by Daniel Suteu, Dec 23 2018