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A027762 Denominator of Sum_{p prime, p-1 divides 2*n} 1/p. 8

%I #26 Feb 22 2022 15:30:35

%S 6,30,42,30,66,2730,6,510,798,330,138,2730,6,870,14322,510,6,1919190,

%T 6,13530,1806,690,282,46410,66,1590,798,870,354,56786730,6,510,64722,

%U 30,4686,140100870,6,30,3318,230010,498,3404310,6,61410,272118,1410,6,4501770

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

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

%C Same as A002445.

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

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

%H R. Mestrovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Mestrovic/mes4.html">On a Congruence Modulo n^3 Involving Two Consecutive Sums of Powers</a>, Journal of Integer Sequences, Vol. 17 (2014), 14.8.4.

%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli numbers.</a>

%F a(n) = A002445(n). [_Joerg Arndt_, May 06 2012]

%F a(n) = A027760(2*n). - _Ridouane Oudra_, Feb 22 2022

%o (PARI)

%o a(n)=

%o {

%o my(s=0);

%o forprime (p=2, 2*n+1, if( (2*n)%(p-1)==0, s+=1/p ) );

%o return( denominator(s) );

%o }

%o /* _Joerg Arndt_, May 06 2012 */

%Y Cf. A027761, A006954.

%Y Cf. A027760.

%K nonn,frac

%O 1,1

%A _N. J. A. Sloane_

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)