OFFSET
0,2
COMMENTS
LINKS
R. Mestrovic, On a Congruence Modulo n^3 Involving Two Consecutive Sums of Powers, Journal of Integer Sequences, Vol. 17 (2014), 14.8.4.
EXAMPLE
The decomposition of B_10 is 5/66 = 1-1/2-1/3-1/11. Multiplied by the product 2*3*11=66 of the denominators this becomes 5=66-33-22-6, and the 4 terms on the right hand side become one row of the table.
1;
2,-1;
6,-3,-2;
30,-15,-10,-6;
42,-21,-14,-6;
30,-15,-10,-6;
66,-33,-22,-6;
2730,-1365,-910,-546,-390,-210;
MAPLE
A165908 := proc(n) local i, p; Ld := [] ; pp := 1 ; for i from 1 do p := ithprime(i) ; if (2*n) mod (p-1) = 0 then Ld := [op(Ld), -1/p] ; pp := pp*p ; elif p-1 > 2*n then break; end if; end do: Ld := [A000146(n), op(Ld)] ; [seq(op(i, Ld)*pp, i=1..nops(Ld))] ; end proc: # for n>=2, R. J. Mathar, Jul 08 2011
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]; Join[{1}, Flatten[ Table[row[n], {n, 0, 9}]]] (* Jean-François Alcover_, Aug 09 2012 *)
CROSSREFS
KEYWORD
tabf,sign
AUTHOR
Paul Curtz, Sep 30 2009
EXTENSIONS
Edited by R. J. Mathar, Jul 08 2011
STATUS
approved