cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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,...

Original entry on oeis.org

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

Views

Author

Paul Curtz, Oct 11 2009

Keywords

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.
		

Crossrefs

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

A176546 Bernoulli numerators A000367 with an additional 1 inserted to represent B_1.

Original entry on oeis.org

1, 1, 1, -1, 1, -1, 5, -691, 7, -3617, 43867, -174611, 854513, -236364091, 8553103, -23749461029, 8615841276005, -7709321041217, 2577687858367, -26315271553053477373, 2929993913841559, -261082718496449122051
Offset: 0

Views

Author

Paul Curtz, Apr 20 2010

Keywords

Comments

Equivalent to adding a 1 in front of A000367, or removing zeros in A164555.
(One could also remove zeros in A027641 which would flip the sign of a(1)).
The denominators are in A006954.

Examples

			B_0=1/1, B_1=1/2 "originally", B_2=1/6, B_4=-1/30, B_6=1/42,...
		

Crossrefs

Showing 1-2 of 2 results.