A141056 1 followed by A027760, a variant of Bernoulli number denominators.

1, 2, 6, 2, 30, 2, 42, 2, 30, 2, 66, 2, 2730, 2, 6, 2, 510, 2, 798, 2, 330, 2, 138, 2, 2730, 2, 6, 2, 870, 2, 14322, 2, 510, 2, 6, 2, 1919190, 2, 6, 2, 13530, 2, 1806, 2, 690, 2, 282, 2, 46410, 2, 66, 2, 1590, 2, 798, 2, 870, 2, 354, 2, 56786730, 2, 6, 2, 510, 2, 64722, 2, 30, 2, 4686

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

Cf. A027760, A027642, A176328.

Cf. A164555, A027642, A048993.

Sequence in context: A217448 A280705 A027760 * A141498 A284004 A225481

Adjacent sequences: A141053 A141054 A141055 * A141057 A141058 A141059

Keyword

nonn

Author

Paul Curtz, Aug 01 2008

Extensions

Extended by R. J. Mathar, Nov 22 2009

Status

approved