A027762 Denominator of Sum_{p prime, p-1 divides 2*n} 1/p.

6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530, 1806, 690, 282, 46410, 66, 1590, 798, 870, 354, 56786730, 6, 510, 64722, 30, 4686, 140100870, 6, 30, 3318, 230010, 498, 3404310, 6, 61410, 272118, 1410, 6, 4501770

Offset

1,1

Comments

From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.

Same as A002445.

References

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.

H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.

Links

Table of n, a(n) for n=1..48.

R. Mestrovic, On a Congruence Modulo n^3 Involving Two Consecutive Sums of Powers, Journal of Integer Sequences, Vol. 17 (2014), 14.8.4.

Index entries for sequences related to Bernoulli numbers.

Formula

a(n) = A002445(n). [Joerg Arndt, May 06 2012]

a(n) = A027760(2*n). - Ridouane Oudra, Feb 22 2022

Prog

(PARI)
a(n)=
{
    my(s=0);
    forprime (p=2, 2*n+1, if( (2*n)%(p-1)==0, s+=1/p ) );
    return( denominator(s) );
}
/* Joerg Arndt, May 06 2012 */

Crossrefs

Cf. A027761, A006954.

Cf. A027760.

Sequence in context: A334900 A136375 A138706 * A002445 A151711 A130512

Adjacent sequences: A027759 A027760 A027761 * A027763 A027764 A027765

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved