A166306 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,...

1, 5, 31, 41, 31, 61, 3421, 5, 557, 821, 371, 121, 3421, 5, 929, 15745, 557, 5, 2557843, 5, 15541, 1805, 743, 241, 60887, 61, 1673, 821, 929, 301, 79085411, 5, 557, 66961, 31, 4397, 188641729, 5, 31, 3281, 277727, 421, 4462547, 5, 66817, 313477, 1487, 5, 5952449, 5

Offset: 1

Author

Paul Curtz, Oct 11 2009

Keywords

• nonn

Comments

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

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

Apparently a(n) = A027761(n+1) for n>=1. - Joerg Arndt, May 06 2012

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A080092, A002445, A165226.

Programs

Mathematica

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 *)

Extensions

Edited and extended by R. J. Mathar, Jul 08 2011

Extended to 50 terms by Jean-François Alcover, Aug 09 2012