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A100652 Denominator of 1 - Sum_{i=1..n} |Bernoulli(i)|.

%I A100652 #13 Jan 28 2013 10:36:05
%S A100652 1,2,3,3,10,10,105,105,70,70,1155,1155,1430,1430,2145,2145,24310,
%T A100652 24310,4849845,4849845,58786,58786,2028117,2028117,965770,965770,
%U A100652 1448655,1448655,28007330,28007330,100280245065,100280245065,66853496710,66853496710,100280245065
%N A100652 Denominator of 1 - Sum_{i=1..n} |Bernoulli(i)|.
%C A100652 Contribution from _Paul Curtz_, Aug 07 2012 (Start):
%C A100652 Take a(0)=1. Then instead of the Akiyama-Tanigawa algorithm we create the extended (or prolonged) Akiyama-Tanigawa algorithm using A028310(n)=1,1,2,3,4,5,... instead of A000027(n)=1,2,3,4,5,.. .
%C A100652 Hence the array (A051714 with an additional column)
%C A100652 2,       1,   1/2,   1/3,     1/4,
%C A100652 1,     1/2,   1/3,   1/4,     1/5,
%C A100652 1/2,   1/6,   1/6,   3/20,   2/15,       A026741(n+1)/A045896(n+1)
%C A100652 1/3,     0,  1/30,   1/20,   2/35,       A194531(n)/A193220(n)
%C A100652 1/3, -1/30, -1/30, -3/140, -1/105.       A051722(n)/A051723(n).
%C A100652 a(n) is the denominator of the (first) column before the Akiyama-Tanigawa algorithm leading to the second Bernoulli numbers A164555(n)/A027642(n). See A176672(n).
%C A100652 (End)
%H A100652 Harvey P. Dale, <a href="/A100652/b100652.txt">Table of n, a(n) for n = 1..1000</a>
%e A100652 1, 1/2, 1/3, 1/3, 3/10, 3/10, 29/105, 29/105, 17/70, 17/70, 193/1155, 193/1155, -123/1430, -123/1430, -2687/2145, -2687/2145, -202863/24310, -202863/24310, -307072861/4849845, ... = A100651/A100652.
%t A100652 Denominator[1-(Accumulate[Abs[BernoulliB[Range[0,40]]]])] (* _Harvey P. Dale_, Jan 28 2013 *)
%K A100652 nonn,frac
%O A100652 1,2
%A A100652 _N. J. A. Sloane_, Dec 05 2004