Search: id:A113184
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%I A113184
%S A113184 1,1,4,5,6,4,8,13,13,6,12,20,14,8,24,29,18,13,20,30,32,12,24,52,31,14,
%T A113184 40,40,30,24,32,61,48,18,48,65,38,20,56,78,42,32,44,60,78,24,48,116,57,
%U A113184 31,72,70,54,40,72,104,80,30,60,120,62,32,104,125,84,48,68,90,96,48,72
%N A113184 Difference between sum of odd divisors of n and sum of even divisors 
               of n.
%C A113184 The generating function equals 1/8 at q = Lambda = 0.1076539192... (A072558) 
               the "One-Ninth" constant. - Michael Somos Jul 21 2006
%H A113184 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               One-NinthConstant.html">Link to a section of The World of Mathematics.</
               a>
%F A113184 Multiplicative with a(2^e) = 2^(e+1)-3 if e>0, a(p^e) = (p^(e+1)-1)/(p-1) 
               if p>2.
%F A113184 G.f.: Sum_{k>0} -(-x)^k/(1+(-x)^k)^2 = Sum_{k>0} k*x^k/(1-(-x)^k).
%F A113184 Expansion of (1-(2/pi)^2(2E(k)-K(k))K(k))/8 in powers of nome q where 
               E(k) and K(k) are complete elliptic integrals and q=exp(-pi*K(k')/
               K(k)). - Michael Somos Jul 21 2006
%o A113184 (PARI) a(n)=if(n<1, 0, (-1)^n*sumdiv(n,d,(-1)^d*d))
%o A113184 (PARI) {a(n)=local(A,p,e); if(n<1, 0, A=factor(n); prod(k=1,matsize(A)[1], 
               if(p=A[k,1], e=A[k,2]; if(p==2, 2^(e+1)-3, (p^(e+1)-1)/(p-1)))))}
%Y A113184 Cf. A002129(n)=-(-1)^n a(n).
%Y A113184 Sequence in context: A016719 A090370 A002129 this_sequence A136004 A134299 
               A112780
%Y A113184 Adjacent sequences: A113181 A113182 A113183 this_sequence A113185 A113186 
               A113187
%K A113184 nonn,mult
%O A113184 1,3
%A A113184 Michael Somos, Oct 17 2005

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