OFFSET
0,2
COMMENTS
The denominators of the Bernoulli numbers for n>0. B_n sequence begins 1, -1/2, 1/6, 0/2, -1/30, 0/2, 1/42, 0/2, ... This is an alternative version of A027642 suggested by the theorem of Clausen. - Peter Luschny, Apr 29 2009
Let f(n,k) = gcd { multinomial(n; n1, ..., nk) | n1 + ... + nk = n }; then a(n) = f(N,N-n+1)/f(N,N-n) for N >> n. - Mamuka Jibladze, Mar 07 2017
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..10080
Thomas Clausen, Lehrsatz aus einer Abhandlung Über die Bernoullischen Zahlen, Astr. Nachr. 17 (22) (1840), 351-352.
Wikipedia, Bernoulli number
FORMULA
a(n) are the denominators of the polynomials generated by cosh(x*z)*z/(1-exp(-z)) evaluated x=1. See A176328 for the numerators. - Peter Luschny, Aug 18 2018
a(n) = denominator(Sum_{j=0..n} (-1)^(n-j)*j!*Stirling2(n,j)*B(j)), where B are the Bernoulli numbers A164555/A027642. - Fabián Pereyra, Jan 06 2022
EXAMPLE
The rational values as given by the e.g.f. in the formula section start: 1, 1/2, 7/6, 3/2, 59/30, 5/2, 127/42, 7/2, 119/30, ... - Peter Luschny, Aug 18 2018
MAPLE
Clausen := proc(n) local S, i;
S := numtheory[divisors](n); S := map(i->i+1, S);
S := select(isprime, S); mul(i, i=S) end proc:
seq(Clausen(i), i=0..24);
# Peter Luschny, Apr 29 2009
A141056 := proc(n)
if n = 0 then 1 else A027760(n) end if;
end proc: # R. J. Mathar, Oct 28 2013
MATHEMATICA
a[n_] := Sum[ Boole[ PrimeQ[d+1]] / (d+1), {d, Divisors[n]}] // Denominator; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Aug 09 2012 *)
PROG
(PARI)
A141056(n) =
{
p = 1;
if (n > 0,
fordiv(n, d,
r = d + 1;
if (isprime(r), p = p*r)
)
);
return(p)
}
for(n=0, 70, print1(A141056(n), ", ")); /* Peter Luschny, May 07 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Aug 01 2008
EXTENSIONS
Extended by R. J. Mathar, Nov 22 2009
STATUS
approved