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Numbers n such that the denominator of BernoulliB(n) is a record.
5

%I #20 Feb 16 2025 08:32:55

%S 0,1,2,4,6,10,12,30,36,60,72,108,120,144,180,240,360,420,540,840,1008,

%T 1080,1200,1260,1620,1680,2016,2160,2520,3360,3780,5040,6480,7560,

%U 8400,10080,12600,15120,25200,30240,42840,45360,55440,60480,75600,85680,100800

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

%H Daniel Suteu, <a href="/A100195/b100195.txt">Table of n, a(n) for n = 1..90</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BernoulliNumber.html">Bernoulli Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Von_Staudt%E2%80%93Clausen_theorem">Von Staudt-Clausen theorem</a>

%o (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))

%o lista(n) = { my(m=0); for(k=0, n, my(d=b(k)); if(d>m, m=d; print1(k, ", "))); }

%o lista(100000); \\ _Daniel Suteu_, Dec 23 2018

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

%K nonn,changed

%O 1,3

%A _Eric W. Weisstein_, Nov 08 2004

%E Corrected and extended by _Daniel Suteu_, Dec 23 2018