

A166306


Denominator of Bernoulli_n multiplied by the sum of the associated inverse primes in the StaudtClausen theorem, n=1, 2, 4, 6, 8, 10,...


1



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
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OFFSET

1,2


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


LINKS

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


EXAMPLE

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.


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[n1] // Rest, Negative]]; Table[a[n], {n, 1, 50}] (* JeanFrançois Alcover, Aug 09 2012 *)


CROSSREFS

Cf. A080092, A002445, A165226.
Sequence in context: A354881 A162173 A027761 * A341632 A287300 A162665
Adjacent sequences: A166303 A166304 A166305 * A166307 A166308 A166309


KEYWORD

nonn


AUTHOR

Paul Curtz, Oct 11 2009


EXTENSIONS

Edited and extended by R. J. Mathar, Jul 08 2011
Extended to 50 terms by JeanFrançois Alcover, Aug 09 2012


STATUS

approved



