A176591 Bernoulli denominators A141056(n), with the exception a(1)=1.

1, 1, 6, 2, 30, 2, 42, 2, 30, 2, 66, 2, 2730, 2, 6, 2, 510, 2, 798, 2, 330, 2, 138, 2, 2730, 2, 6, 2, 870, 2, 14322, 2, 510, 2, 6, 2, 1919190, 2, 6, 2, 13530, 2, 1806, 2, 690, 2, 282, 2, 46410, 2, 66, 2, 1590, 2, 798, 2, 870, 2, 354, 2, 56786730, 2, 6, 2, 510, 2, 64722, 2, 30, 2, 4686, 2, 140100870, 2, 6, 2, 30, 2

Offset: 0

Author

Paul Curtz, Apr 21 2010

Keywords

• nonn
• frac

Comments

These are also the denominators of a sequence generated by inverse binomial transform of a modified Bernoulli sequence described in (with numerators in) A176328.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..4096

Crossrefs

Cf. A141056, A160014.

Programs

Maple

read("transforms") ; evb := [1, 0, seq(bernoulli(n), n=2..50)] ; BINOMIALi(evb) ; apply(denom, %) ; # R. J. Mathar, Dec 01 2010
seq(denom((bernoulli(i,1)+bernoulli(i,2))/2),i=0..50); # Peter Luschny, Jun 17 2012

Mathematica

a[n_] := If[OddQ[n], 2, BernoulliB[n] // Denominator]; a[1] = 1; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Dec 29 2012 *)
Join[{1,1},BernoulliB[Range[2,80]]/.(0->1/2)//Denominator] (* Harvey P. Dale, Dec 31 2018 *)

PARI

A176591(n) = { my(p=1); if(n>1, fordiv(n, d, my(r=d+1); if(isprime(r), p = p*r))); return(p); }; \\ Antti Karttunen, Dec 20 2018, after code in A141056

Formula

a(n) = A141056(n), n <> 1.

a(n) = A027760(n), n>1.

a(2n) = A002445(n), a(2n+1)= A040000(n).

Extensions

More terms from Antti Karttunen, Dec 20 2018