A176591 - OEIS

%I #22 Dec 31 2018 11:35:17

%S 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,

%T 2,6,2,870,2,14322,2,510,2,6,2,1919190,2,6,2,13530,2,1806,2,690,2,282,

%U 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

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

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

%H Antti Karttunen, <a href="/A176591/b176591.txt">Table of n, a(n) for n = 0..4096</a>

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

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

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

%p read("transforms") ; evb := [1, 0, seq(bernoulli(n), n=2..50)] ; BINOMIALi(evb) ; apply(denom, %) ; # _R. J. Mathar_, Dec 01 2010

%p seq(denom((bernoulli(i,1)+bernoulli(i,2))/2),i=0..50); # _Peter Luschny_, Jun 17 2012

%t a[n_] := If[OddQ[n], 2, BernoulliB[n] // Denominator]; a[1] = 1; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Dec 29 2012 *)

%t Join[{1,1},BernoulliB[Range[2,80]]/.(0->1/2)//Denominator] (* _Harvey P. Dale_, Dec 31 2018 *)

%o (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

%Y Cf. A141056, A160014.

%K nonn,frac

%O 0,3

%A _Paul Curtz_, Apr 21 2010

%E More terms from _Antti Karttunen_, Dec 20 2018