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

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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

• 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.

Crossrefs

Cf. A027761, A006954.

Cf. A027760.

Programs

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 */

Formula

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

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