A166306 - OEIS

%I #19 Jun 20 2016 02:57:56

%S 1,5,31,41,31,61,3421,5,557,821,371,121,3421,5,929,15745,557,5,

%T 2557843,5,15541,1805,743,241,60887,61,1673,821,929,301,79085411,5,

%U 557,66961,31,4397,188641729,5,31,3281,277727,421,4462547,5,66817,313477,1487,5,5952449,5

%N Denominator of Bernoulli_n multiplied by the sum of the associated inverse primes in the Staudt-Clausen theorem, n=1, 2, 4, 6, 8, 10,...

%C This is the absolute value of the sum of the negative terms in row n of triangle A165908.

%C It appears that a(n) mod 9 is always one of {1, 2, 4, 5, 7, 8}.

%C Apparently a(n) = A027761(n+1) for n>=1. - _Joerg Arndt_, May 06 2012

%H T. D. Noe, <a href="/A166306/b166306.txt">Table of n, a(n) for n = 1..1000</a>

%e The primes associated with B_10 = 5/66 are 2, 3 and 11. 66*(1/2+1/3+1/11) = 33+22+6 = 61 is the representative in this sequence.

%t a146[n_] := Sum[ Boole[ PrimeQ[d+1]]/(d+1), {d, Divisors[2n]}] + BernoulliB[2n]; primes[n_] := Select[ Prime /@ Range[n+1], Divisible[2n, #-1]&]; row[n_] := With[{pp = primes[n]}, Join[{a146[n]}, -1/pp]*Times @@ pp]; a[n_] := -Total[ Select[ row[n-1] // Rest, Negative]]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Aug 09 2012 *)

%Y Cf. A080092, A002445, A165226.

%K nonn

%O 1,2

%A _Paul Curtz_, Oct 11 2009

%E Edited and extended by _R. J. Mathar_, Jul 08 2011

%E Extended to 50 terms by _Jean-François Alcover_, Aug 09 2012